Cutting polytera

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

Cutting polytera

Postby Marek14 » Mon Feb 25, 2013 7:43 pm

Trying to cut 5D figures:

(3,3,3,3) set:

10000 - no cuts, verf is unit pentachoron

01000 - verf is tetrahedral prism with unit edge. It's therefore possible to cut off a (point || tetrahedral prism) (two pentachora, four triangular prismatic pyramids (cuts of rectified pentachora), one tetrahedral prism)). Rest is octahedron || tetrahedral prism, with 1 tetrahedral prism, 2 rectified pentachora, 4 (triangle || dual triangular prism) - cuts of rectified pentachora, and 4 pentachora.
It can be also cut in two identical halves (triangle || dual triangular duoprism). Each of these has 3 (triangle || dual triangular prism), 3 triangular prismatic pyramids and 3 pentachora.
Some Johnson solids might be possible by gluing the triangular duoprisms back together wrong.

00100 - verf is unit triangular duoprism.
One possible cut is into two identical halves (tetrahedron || octahedral prism). Each half has 1 octahedral prism, 2 rectified pentachora, 4 triangular prismatic pyramids and 4 (triangle || dual triangular prism).
There might be an "orthododecateron" formed by gluing the octahedral prisms wrong?
Another option is to cut "vertex first". Dodecateron is tristratic here and forms two triangular duoprismatic pyramids and a (triangular duoprism || twice dual triangular duoprism [each of its base triangles is dual to a base triangle of the other duoprism]). This segmentoteron has 2 triangular duoprisms, and 12 (triangle || dual triangular prism)

11000 - verf is tetrahedral pyramid with unit base and r(6) side edges. No simple cuts with unit edges.

10100
Bistratic, can be cut into rectified pentachoron || truncated pentachoron (1 rectified pentachoron, 1 truncated pentachoron, 5 (octahedron || truncated tetrahedron) - cut of small rhombated pentachoron, 5 tetrahedral prisms) and small rhombated pentachoron || truncated pentachoton (1 small rhombated pentachoron, 1 truncated pentachoron, 5 (cuboctahedron || truncated tetrahedron) - cut of small rhombated pentachoron, 5 rectified pentachora, 5 tetrahedral prisms).
It's also possible to cut off a cap (triangle || (6,3)-duoprism) with 1 (3,6)-duoprism, 3 (triangle || hexagonal prism), 3 tetrahedral prisms and 3 triangular prismatic pyramids. This cap might be available for gyration.
Finally, a cap (cuboctahedron || truncated tetrahedral prism) can be cut off. This cap has 1 truncated tetrahedral prism, 2 (cuboctahedron || truncated tetrahedron), 4 (triangle || hexagonal prism), 4 (triangle || dual triangular prism) and 6 tetrahedral prisms.

10010
Bistratic, can be cut into (rectified pentachoron || dual small rhombated pentachoron) with 1 rectified pentachoron, 1 small rhombated pentachoton, 5 (tetrahedron || cuboctahedron) - half of small prismated decachoron, 5 octahedral prisms and 10 triangular duoprisms, and (small prismated decachoron || small rhombated pentachoron) with 1 small prismated decachoron, 1 small rhombated pentachoron, 5 (tetrahedron || cuboctahedron), 5 rectified pentachora, 10 triangular duoprisms and 10 octahedral prisms.
You can also cut off a cap (tetrahedron || cuboctahedral prism) which has 1 cuboctahedral prism, 2 (tetrahedron || cuboctahedron), 4 triangular duoprisms, 4 triangular prismatic pyramids and 6 square pyramid prisms. Gyration of this cap might be possible.

10001
Bistratic, can be cut in half, each half is (pentachoron || small prismated decachoron) with 6 pentachora (1 base, 5 lateral), 1 small prismated decachoron, 15 tetrahedral prisms (5 as tetrahedron || tetrahedron, 10 as line || triangular prism) and 10 triangular duoprisms. Might be possible to gyrate the halves.

01100
No simple cuts

01010
Bistratic, can be cut in half, each half is (small rhombated pentachoron || decachoron) with 1 small rhombated pentachoron, 1 decachoron, 5 (cuboctahedron || truncated tetrahedron), 5 (octahedron || truncated tetrahedron) and 10 triangular duoprisms. Might be possible to gyrate the halves.
It's possible to cut off a cap (octahedron || truncated tetrahedral prism) with 1 truncated tetrahedral prism, 2 (octahedron || truncated tetrahedron), 4 triangular duoprisms and 4 (triangle || hexagonal prism).

11100
No simple cuts

11010
You can cut off a cupola (prismatotruncated pentachoron || great rhombated pentachoron) with 1 prismatotruncated pentachoron, 1 great rhombated pentachoron, 5 (truncated tetrahedron || truncated octahedron) - cut of prismatotruncated pentachoron, 5 (cuboctahedron || truncated tetrahedron), 10 otahedral prisms and 10 (3,6)-duoprisms.
You can also cut off a cap (truncated tetrahedron || truncated octahedral prism) with 1 truncated octahedral prism, 2 (truncated tetrahedron || truncated octahedron), 4 (3,6)-duoprisms, 4 (triangle || hexagonal prism) and 6 square pyramidal prisms.

11001
You can cut off a cupola (truncated pentachoron || prismatotruncated pentachoron) with 1 truncated pentachoron, 1 prismatotruncated pentachoron, 5 truncated tetrahedral prisms, 5 (tetrahedron || cuboctahedron), 10 (3,6)-duoprisms and 10 tetrahedral prisms.

10110
You can cut off a cupola (decachoron || great rhombated pentachoron) with 1 decachoron, 1 great rhombated pentachoron, 5 (truncated tetrahedron || truncated octahedron), 5 truncated tetrahedral prisms and 10 triangular duoprisms.

10101
Tristratic, formed by 2 cupolas (small rhombated pentachoron || dual prismatotruncated pentachoton) with 1 small rhombated pentachoron, 1 prismatotruncated pentachoron, 5 (octahedron || truncated tetrahedron), 5 cuboctahedral prisms, 10 triangular cupolic prisms and 10 triangular duoprisms. The middle section is (prismatotruncated pentachoron || dual prismatotruncated pentachoron) with 2 prismatotruncated pentachora, 10 (cuboctahedron || truncated tetrahedron) and 20 triangular cupolic prisms.
It's also possible to cut off a cupola (triangular duoprism || hexagonal duoprism), which has 1 triangular duoprism, 1 hexagonal duoprism, 6 (triangle || hexagonal prism) and 6 triangular cupolic prisms. There could exist several possible gyrations.

01110
No simple cuts.

11110
No simple cuts

11101
You can cut off a cupola (great rhombated pentachoron || great prismated decachoron) with 1 great prismated pentachoron, 1 great prismated decachoron, 5 truncated octahedral prisms, 5 (truncated tetrahedron || truncated octahedron), 10 (3,6)-duoprisms and 10 triangular cupolic prisms. Gyration might be possible.

11011
Can be cut in two halves, each half is a bistratic rotunda with 1 prismatotruncated pentachoron, 1 great prismated decachoron, 15 truncated tetrahedral prisms (5 as truncated tetrahedron || truncated tetrahedron, 10 spread among all 3 layers of vertices), 5 (truncated tetrahedron || truncated octahedron), 5 prismatotruncated pentachora with (truncated tetrahedron || truncated octahedron) cupola cut off and 10 hexagonal duoprisms. Gyration might be possible.

11111
No simple cuts
Last edited by Marek14 on Tue Feb 26, 2013 9:17 am, edited 2 times in total.
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Re: Cutting polytera

Postby quickfur » Mon Feb 25, 2013 9:16 pm

One interesting thing about polytera is that even though there is no direct equivalent of the pentagonal polytopes, the 4D pentagonal polytopes *do* feature as planar figures in 5D. This gives rise to all sorts of CRFs built on the 120-cell/600-cell family polychora. For example, there's the 5D ursateron made from a 600-cell, a rectified 600-cell (o5o3x3o), 600 tetrahedral teddies, and 120 icosahedral pyramids.
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Re: Cutting polytera

Postby Klitzing » Mon Feb 25, 2013 11:17 pm

hy Marek,
you missed 01110.
--- rk
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Re: Cutting polytera

Postby Marek14 » Tue Feb 26, 2013 6:45 am

Klitzing wrote:hy Marek,
you missed 01110.
--- rk


Edited -- no simple cuts found.
Also corrected when I realized that "square || inclined square" is actually tetrahedral prism.
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Re: Cutting polytera

Postby Marek14 » Tue Feb 26, 2013 10:31 am

(4,3,3,3) family:

1'0000
No simple cuts

0'1000
Tetrastratic -- can be cut into two cupolas (pentachoron || truncated pentachoron) with 6 pentachora (1 base and 5 lateral), 1 truncated pentachoron and 5 (tetrahedron || truncated tetrahedron) - cuts of rectified tesseract and two segmentotera (truncated pentachoron || decachoron) with 1 truncated pentachoron, 1 decachoron, 5 (truncated tetrahedron || dual truncated tetrahedron) - middle parts of rectified tesseracts, 5 (tetrahedron || truncated tetrahedron) and 10 pentachora. Gyration of two halves of polyteron might be possible.

0'0100
Can be cut in half into two (icositetrachoron || rectified tesseract) with 1 icositetrachoron, 1 rectified tesseract, 8 (octahedron || cuboctahedron) -- half of icositetrachoron and 16 rectified pentachora.
It's also possible to slice off a cap (octahedron || cuboctahedral prism) with 1 cuboctahedral prism, 2 (octahedron || cuboctahedron), 6 cubic prisms -- slices of icositetrachoron and 8 (triangle || dual triangular prism).
Another cap is (3,4) duoprismatic pyramid with 1 (3,4)-duoprism, 3 cubic pyramids and 4 triangular prismatic pyramids.
Finally, you can cut it in three pieces: two cupolas (rectified pentachoron || small rhombated pentachoron) with 6 rectified pentachora (1 base, 5 lateral), 1 small rhombated pentachoron, 5 (octahedron || cuboctahedron), and 10 triangular prismatic pyramids. The middle section is (small rhombated pentachoron || dual small rhombated pentachodon) with 2 small rhombated pentachora, 10 (octahedron || cuboctahedron) and 20 (triangle || dual triangular prism).

0'0010
Can be cut in half in two distinct ways.
One is in two (hexadecachoron || icositetrachoron) with 1 hexadecachoron, 1 icositetrachoron, 8 octahedral pyramids (half of hexadecachoron) and 16 rectified pentachora. Since icositetrachoron has greater symmetry than hexadecachoron, gyration might be possible.
The other one is in two (rectified pentachoron || small prismated decachoron) with 6 rectified pentachora (1 base, 5 lateral), 1 small prismated decachoron, 5 hexadecachora, 5 triangular prismatic pyramids and 5 (triangle || dual triangular prism). Gyration might be possible.
Finally, you can cut off an octahedral prismatic pyramid (1 octahedral prism, 2 octahedral pyramids, 8 triangular prismatic pyramids).

0'0001
Can be cut in two hexadecachoral pyramids (1 hexadecachoron, 16 pentachora).

1'1000
No simple cuts.

1'0100
It can be cut into truncated tesseractic prism and two cupolas (small rhombated tesseract || truncated tesseract) with 1 small rhombated tesseract, 1 truncated tesseract, 8 (rhombicuboctahedron || truncated cube) -- cuts of small rhombated tesseract, 32 tetrahedral prisms and 16 rectified pentachora.
It's possible to cut off a cap (rhombicuboctahedron || truncated cubic prism) with 1 truncated cubic prism, 2 (rhombicuboctahedron || truncated cube), 6 (square || octagonal prism) -- caps of small rhombated tesseract, 12 tetrahedral prisms and 8 (triangle || dual triangular prism).
It's possible to cut off a cap (square || (3,8)-duoprism) with 3 (square || octagonal prism), 4 tetrahedral prisms and 4 triangular prismatic pyramids. Gyration might be possible.

1'0010
It can be cut into small rhombated tesseractic prism and two cupolas (small prismated tesseract || small rhombated tesseract) with 1 small prismated tesseract, 1 small rhombated tesseract, 8 (cube || rhombicuboctahedron) -- cuts of small prismated tesseract, 24 (3,4)-duoprisms, 32 octahedral prisms and 16 rectified pentachora.

1'0001
It can be cut into small prismated tesseractic prism and two cupolas (tesseract || small prismated tesseract) with 9 tesseracts (1 base, 8 lateral), 1 small prismated tesseract, 24 (3,4)-duoprisms, 32 tetrahedral prisms and 16 pentachora.

0'1100
No simple cuts.

0'1010
You can cut off a cupola (rectified icositetrachoron || bitruncated tesseract) with 1 rectified icositetrachoron, 1 bitruncated tesseract, 8 (cuboctahedron || truncated octahedron) -- cuts of rectified icositetrachoron, 24 (3,4)-duoprisms and 16 (cuboctahedron || truncated tetrahedron).
You can cut off a cap (cuboctahedron || truncated octahedral prism) with 1 truncated octahedral prism, 2 (cuboctahedron || truncated octahedron), 6 (3,4)-duoprisms and 8 (triangle || hexagonal prism) -- caps of small rhombated pentachoron.
You can cut off a cupola (small rhombated pentachoron || great rhombated pentachoron) with 1 small rhombated pentachoron, 1 great rhombated pentachoron, 5 (cuboctahedron || truncated octahedron), 10 (3,4)-duoprisms and 5 (octahedron || truncated tetrahedron).

0'1001
You can cut off a cupola (rectified tesseract || rectified icositetrachoron) with 1 rectified tesseract, 1 rectified icositetrachoron, 8 cuboctahedral prisms, 24 (3,4)-duoprisms and 16 (tetrahedron || cuboctahedron). Gyration might be possible.
You can cut off a cupola (small prismated decachoron || prismatotruncated pentachoron) with 1 small prismated decachoron, 1 prismatotruncated pentachoron, 5 (tetrahedron || truncated tetrahedron), 10 triangular cupolic prisms, 10 (3,4)-duoprisms and 5 (tetrahedron || cuboctahedron).

0'0110
Can be cut in two bistratic halves, each one with 1 truncated hexadecachoron, 17 decachora (1 base, 16 lateral) and 8 halves of truncated hexadecachoron.

0'0101
Tetrastratic, can be cut in two cupolas (icositetrachoron || truncated hexadecachoron) with 1 icositetrachoron, 1 truncated hexadecachoron, 8 octahedral prisms and 16 (octahedron || truncated tetrahedron) and 2 segmentotera (truncated hexadecachoron || rectified icositetrachoron) with 1 truncated hexadecachoron, 1 rectified icositetrachoron, 8 (octahedron || cuboctahedron), 24 square pyramid prisms and 16 (cuboctahedron || truncated tetrahedron). Halves might be capable of gyrating.
You can cut off a cap (triangle || (6,4)-duoprism) with 1 (4,6)-duoprism, 3 cubic pyramids, 3 square pyramid prisms and 4 (triangle || hexagonal prism). Gyration might be possible.
You can cut off a cupola (small rhombated pentachoron || dual prismatotruncated pentachoron) with 1 small rhombated pentachoron, 1 prismatotruncated pentachoron, 5 (octahedron || cuboctahedron), 10 octahedral prisms, 10 (triangle || hexagonal prism) and 5 (cuboctahedron || truncated tetrahedron).

0'0011
Can be cut in two bistratic halves, each one with 1 hexadecachoron, 1 truncated hexadecachoron, 8 octahedral pyramids and 16 truncated pentachora.

To be continued...
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Re: Cutting polytera

Postby Marek14 » Tue Feb 26, 2013 10:07 pm

1'1100
No simple cuts.

1'1010
You can cut off a cupola (prismatotruncated tesseract || great rhombated tesseract) with 1 prismatotruncated tesseract, 1 great rhombated tesseract, 8 (truncated tetrahedron || truncated cuboctahedron) -- cuts of prismatotruncated tesseract, 24 (3,8)-duoprisms, 32 octahedral prisms and 16 (cuboctahedron || truncated tetrahedron).
You can cut off a cap (truncated tetrahedron || truncated cuboctahedral prism) with 1 truncated cuboctahedral prism, 2 (truncated tetrahedron || truncated cuboctahedron), 6 (3,8)-duoprisms, 12 square pyramidal prisms and 8 (triangle || hexagonal prism).

1'1001
You can cut off a cupola (truncated tesseract || prismatotruncated tesseract) with 1 truncated tesseract, 1 prismatotruncated tesseract, 8 truncated tetrahedral prisms, 24 (3,8)-duoprisms, 32 tetrahedral prisms and 16 (tetrahedron || cuboctahedron).

1'0110
This polyteron has a central great rhombated tesseractic prism capped by two bistratic cupolas with 1 prismatotruncated hexadecachoron, 1 great rhombated tesseract, 8 bistratic cuts of prismatotruncated hexadecachoron (each has 1 rhombicuboctahedron, 1 truncated cuboctahedron, 6 cubes, 12 hexagonal prisms and 8 truncated tetrahedra), 24 (3,4)-duoprisms, 32 truncated tetrahedral prisms and 16 decachora.

1'0101
Pentastratic -- consists of central prismatotruncated tesseractic prism, two segmentotera (prismatotruncated hexadecachoron || prismatotruncated tesseract) with 1 prismatotruncated hexadecachoron, 1 prismatotruncated tesseract, 8 (rhombicuboctahedron || truncated cube), 24 square cupolic prisms, 32 triangular cupolic prisms and 16 (cuboctahedron || truncated tetrahedron) and two cupolas (small rhombated tesseract || prismatotruncated hexadecachoron) with 1 small rhombated tesseract, 1 prismatotruncated hexadecachoron, 8 rhombicuboctahedral prisms, 24 (3,4)-duoprisms, 32 triangular cupolic prisms and 16 (octahedron || truncated tetrahedron).
You can also cut off a cupola ((3,4)-duoprism || (6,8)-duoprism) with 1 (3,4)-duoprism, 1 (6,8)-duoprism, 3 (square || octagonal prism), 3 square cupolic prisms, 4 triangular cupolic prisms and 4 (triangle || hexagonal prism).

1'0011
Central prismatotruncated hexadecachoric prism is capped by two bistratic cupolas with 1 small prismated tesseracti, 1 prismatotruncated hexadecachoron, 8 tesseracts, 8 (cube || rhombicuboctahedron), 24 (4,6)-duoprisms, 32 truncated tetrahedral prisms and 16 truncated pentachora.

0'1110
No simple cuts.
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Re: Cutting polytera

Postby Marek14 » Thu Feb 28, 2013 5:14 pm

0'1101
You can cut off a cap (bitruncated tesseract || truncated icositetrachoron) with 1 bitruncated tesseract, 1 truncated icositetrachoron, 8 truncated octahedral prisms, 24 (3,4)-duoprisms and 16 (truncated tetrahedron || truncated octahedron). Gyration might be possible.

0'1011
You can cut off a bistratic cupola with 1 rectified icositetrachoron, 1 truncated icositetrachoron, 8 cuboctahedral prisms, 8 (cuboctahedron || truncated octahedron), 24 (4,6)-duoprisms and 16 bistratic cupolas (cuboctahedron-truncated octahedron) -- parts of prismatotruncated pentachoron.
You can also cut off a cupola (prismatotruncated pentachoron || great prismated decachoron) with 1 prismatotruncated pentachoron, 1 great prismated decachoron, 5 (truncated tetrahedron || truncated octahedron), 10 (4,6)-duoprisms, 10 triangular cupolic prisms and 5 (cuboctahedron || truncated octahedron). Gyration might be possible.

0'0111
Can be cut in two tristratic halves with 1 truncated hexadecachoron, 1 truncated icositetrachoron, 8 octahedral prisms, 8 halves of truncated hexadecachoron, 24 square-pyramidal prisms and 16 great rhombated pentachora. Gyration might be possible.

1'1110
No simple cuts.

1'1101
You can cut off a cupola (great rhombated tesseract || great prismated tesseract) with 1 great rhombated tesseract, 1 great prismated tesseract, 8 truncated cuboctahedral prisms, 24 (3,8)-duoprisms, 32 triangular cupolic prisms and 16 (truncated tetrahedron || truncated octahedron).

1'1011
You can cut off a bistratic cupola with 1 prismatotruncated tesseract, 1 great prismated tesseract, 8 truncated cubic prisms, 8 (truncated cube || truncated cuboctahedron), 24 (6,8)-duoprisms, 32 truncated tetrahedral prisms and 16 parts of prismatotruncated pentachoron (with truncated tetrahedron || truncated octahedron cut off).

1'0111
Central great prismated tesseractic prism is capped by two tristratic cupolas with 1 prismatotruncated hexadecachoron, 1 great prismated tesseract, 8 rhombicuboctahedral prisms, 8 bistratic cupolas with (1 rhombicuboctahedron, 1 truncated cuboctahedron, 6 cubes, 6 square cupolas, 12 hexagonal prisms and 8 truncated tetrahedra) -- cuts of prismatotruncated hexadecachoron, 24 (4,6)-duoprisms, 24 square cupolic prisms, 32 truncated octahedral prisms and 16 great rhombated pentachora.

0'1111
No simple cuts

1'1111
No simple cuts
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Re: Cutting polytera

Postby Marek14 » Mon Mar 04, 2013 3:58 pm

Hemipenteractic group
Legend: since the two single nodes going from the branch are always 1 and 0 (otherwise the polyteron reduces to something from penteract group), I only show the three remaining nodes.

000
Can be cut in two halves (tetrahedron || dual tetrahedral prism) with 2 hexadecachora, 6 square duopyramids, 4 pentachora and 4 triangular prismatic pyramids.
You can also cut off a rectified pentachoric pyramid (1 rectified pentachoron, 5 pentachora and 5 octahedral prisms), leaving (pentachoron || dual rectified pentachoron) with 11 pentachora (1 base, 10 lateral), 1 rectified pentachoron, 5 hexadecachora and 5 octahedral prisms.
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Re: Cutting polytera

Postby Klitzing » Mon Mar 04, 2013 5:31 pm

Marek14 wrote:Hemipenteractic group
Legend: since the two single nodes going from the branch are always 1 and 0 (otherwise the polyteron reduces to something from penteract group), I only show the three remaining nodes.

000
[...]


In that special case, there is no ambiguity. But generally: do you imply the 1 and 0 branches to be emanating from the right or the left of the displayed reminder?

--- rk
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Re: Cutting polytera

Postby Klitzing » Mon Mar 04, 2013 6:12 pm

Ahh, speaking of hin, that one should be possible to provide the segmentotera oct||hex and tet||rap as well! (Both of which in fact are the same solid, just displayed in other directions.) Its cells would be 1 hex, 2 rap, 8 octpy, and 6 pen

In fact, hin can be given as lace prism as x3o3o *b3o||o3o3x *b3o, i.e. as hex||gyro hex. (Note that hex is the alternation of tes, and hin therefore is the alternation of pent = tes||tes. So we indeed have 2 gyrated copies of hex.) Accordingly its lace city is
Code: Select all
o3o3o   o3x3o   o3o3o
                    
    x3o3o   o3o3x   

and that of the just described one then is just the bidiminishing thereof:
Code: Select all
    o3x3o   
            
x3o3o   o3o3x


That bidiminished fellow even has a nice description as lace simplex (in fact: in here its a lace triangle): xoo3oxo3oox&#x.

--- rk
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Re: Cutting polytera

Postby Marek14 » Mon Mar 04, 2013 8:13 pm

I presume the alternate vertices on the left.
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Re: Cutting polytera

Postby Klitzing » Mon Mar 04, 2013 9:56 pm

left?
--- rk
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Re: Cutting polytera

Postby Marek14 » Mon Mar 04, 2013 11:48 pm

Klitzing wrote:left?
--- rk


To the left of the displayed :)
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Re: Cutting polytera

Postby Klitzing » Tue Mar 05, 2013 9:30 pm

Hein?

It is a BI-diminishing. Accordingly it is diminished at 2 places. In this case: at 2 vertices.
Code: Select all
o3o3o = point
x3o3o = tet
o3o3x = tet in relatively dual positioning
o3x3o = oct

Thus:
Code: Select all
o3o3o || o3x3o || o3o3o = hex
x3o3o || o3o3x = hex in relatively gyrated positioning

And
Code: Select all
hex || gyro hex = hin


In fact, you've to diminish the top hex from both sides down to its central oct, whereas the bottom hex only gets scratched at its pair of opposite tets. - In total this is chopping off 2 rap-pyramids.

With resp. to my display (those lace cities): it gets diminished from the left and from the right. Keeping the central part, that triangular shaped lace city.

--- rk
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Re: Cutting polytera

Postby Marek14 » Wed Mar 06, 2013 8:10 am

Yup, I know about the hex || gyrated hex -- I don't mention these things since they are not "cuts" :)

(10)100
Can be cut in two parts.
First part is a tristratic (truncated pentachoron || dual great rhombated pentachoron). This has 11 truncated pentachora (1 base, 10 lateral), 1 great rhombated pentachoron, 5 truncated hexadecachora, 10 (triangle || dual triangular prism), 5 rectified pentachora and 5 bistratic (octahedron || truncated octahedron) -- halves of truncated hexadecachoron.
Second part is a bistratic (rectified pentachoron || great rhombated pentachoron). This half has 1 rectified pentachoron, 1 great rhombated pentachoron, 5 bistratic (octahedron || truncated octahedron), 10 triangular prismatic pyramids and 5 truncated pentachora.
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Re: Cutting polytera

Postby Klitzing » Wed Mar 06, 2013 12:04 pm

Marek14 wrote:Yup, I know about the hex || gyrated hex -- I don't mention these things since they are not "cuts" :)


Yep, these are lace prism (or more generally lace tower) descriptions. You even can find some valueable infos from lace cities (as I already provided here).

That mentioned figure, being a bidiminishing, clearly was a cut applied to a cut.

Suppose your "cuts" thereas are ment to be multistratic segments, being directly obtained from uniform figures, only? I.e. using 2 parallel vertex layers for boundary only?

It was this allowance of further diminishings, augmentations, gyrations, ... (in fact: any possible stacking of base objects) which expanded my segmentotope definition beyond that of Wendy's (unit-edged) lace prisms.

--- rk
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Re: Cutting polytera

Postby Marek14 » Wed Mar 06, 2013 1:00 pm

Well, for now I was just trying basic cuts to get some feel for the polytera. I know about lace towers and cities, but for this I'm not looking at them; I'm trying to derive them from scratch to get more acquainted with them :)
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Re: Cutting polytera

Postby username5243 » Sun Nov 04, 2018 1:20 pm

Just realized this list never was completed. I've tried to complete it below, not sure if I got them all, but I think this is most of the rest:

(10)010

Tristratic - consists of two rectified tesseract || truncated hexadecachoron (1 rectified tesseract, 1 truncated hexadecachoron, 8 truncated tetrahedron || cuboctahedron, 8 tetrahedron || truncated tetrahedron, and 8 rectified pentachora) and central truncated hexadecachoron || gyrated truncated hexadecachoron (2 truncated hexadecachora, 16 octahedron || truncated tetrahedron, 8 truncated tetrahedron || dual truncated tetrahedron).

You can cut off rectified pentachoron || decachoron with 1 rectified pentachoron, 1 decachoron, 5 tetrahedron || truncated tetrahedron, and5 octahedron || truncated tetrahedron. The next layer under this subsymmetry is decachoron || prismatorhombated pentachoron (1 decachoron, 1 prismatorhombated pentachoron, 5 cuboctahedron || truncated tetrahedron, 5 truncated tetrahedron || dual truncated tetrahedron, 10 triangle || dual triangular prism, 10 triangle || hexagonal prism).

finally, you can cut off tetrahedron || truncated tetrahedral prism with 1 truncated tetrahedral prism, 2 tetrahedron || truncated tetrahedron, 4 triangle || hexagonal prism, and 4 triangular prismatic pyramids.

(10)001

Tristratic - can be cut into 2 hexadecachoron || rectified tesseract (1 hexadecachoron, 1 rectified tesseract, 8 tetrahedron || cuboctahedron, 8 pentachora, 8 tetrahedral prisms) and a central rectified tesseract || gyrated rectified tesseract (2 rectified tesseract, 16 tetrahedron || cuboctahedron, 8 hexadecachora, 24 tetrahedral prisms).

Also has cap pentachoron || small rhombated pentachoron (1 pentachoron, 1 small rhombated pentachoron, 5 tetrahedron || cuboctahedron, 5 octahedral pyramids, 10 tetrahedral prisms).

(10)110

No cuts.

(10)101

Can cut off truncated hexadecachoron || bitruncated tesseract (1 truncated hexadecachoron, 1 bitruncated tesseract, 8 truncated tetrahedron || truncated octahedron, 8 truncated tetrahedral prisms, 8 octahedron || truncated tetrahedron).

Also can cut off a bistratic small rhombated pentachoron || great prismatodecachoron (1 small rhombated pentachoron, 1 great prismatodecachoron, 5 octahedral rotundas, 5 diminished prismatorhombated pentachora, 10 truncated tetrahedral prisms, 10 triangle || hexagonal prism).

(10)011

Can be cut into three pieces: outer pieces are bistratic rectified tesseract || bitruncated tesseract (1 rectified tesseract, 1 bitruncated tesseract, 8 diminished prismatorhombated pentachora, 8 truncated pentachora, 8 tetrahedral prisms, 8 tetrahedron || truncated tetrahedron), while inner piece is bitruncated tesseract || gyrated bitruncated tesseract (2 bitruncated tesseracts, 16 truncated tetrahedron || truncated octahedron, 8 truncated tetrahedron || dual truncated tetrahedron, 24 tetrahedral prisms).

Can also cut off truncated pentachoron || great rhombated pentachoron (1 truncated pentachoron, 1 great rhombated pentachoron, 5 truncated tetrahedron || truncated octahedron, 5 tetrahedron || truncated tetrahedron, 10 tetrahedral prisms).

(10)111

No cuts.

Also, there was at least one missing on the original list - 1'0010 should have a cap of cube || rhombicuboctahedral prism, similar to 10010's cap of tetrahedron || cuboctahedral prism. This cap has 1 rhombicuboctahedral prism, 2 cube || rhombicuboctahedron, 6 (3,4)-duoprisms, 8 triangular prismatic pyramids, and 12 square pyramidal prisms.
username5243
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