by 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.