- Code: Select all
A
/ \
/ \
/ \
B-------C
A = x3o3o *b3o
B = o3o3x *b3o
C = o3o3o *b3x
Has this been found before? Similar shapes can be made from the rectified tesseract, truncated hexadecachoron, etc.
A
/ \
/ \
/ \
B-------C
A = x3o3o *b3o
B = o3o3x *b3o
C = o3o3o *b3x
polychoronlover wrote:Today I found that a polypeton could be constructed by taking the convex hull of three hexadecachora in different orientations, each having demitesseractic symmetry, in parallel flunes arranged like the vertices of an equilateral triangle.
I think it is scaliform. It has 3 hemipenteracts and 24 (I think) hexadecachoric pyramids, and possibly other facets too.
xoo3ooo3oxo *b3oox&#x
o..3o..3o.. *b3o.. & | 24 | 6 8 | 12 36 12 | 8 32 12 48 | 1 8 10 20 30 | 2 9 6
------------------------+----+-------+-----------+---------------+----------------+--------
x.. ... ... ... & | 2 | 72 * | 4 4 0 | 4 8 2 4 | 1 4 4 4 4 | 2 4 1
oo.3oo.3oo. *b3oo.&#x & | 2 | * 96 | 0 6 3 | 0 6 3 15 | 0 3 2 7 12 | 1 5 3
------------------------+----+-------+-----------+---------------+----------------+--------
x..3o.. ... ... & | 3 | 3 0 | 96 * * | 2 2 0 0 | 1 2 2 1 0 | 2 2 0
xo. ... ... ...&#x & | 3 | 1 2 | * 288 * | 0 2 1 2 | 0 2 1 2 3 | 1 3 1
ooo3ooo3ooo *b3ooo&#x | 3 | 0 3 | * * 96 | 0 0 0 6 | 0 0 0 3 6 | 0 3 2
------------------------+----+-------+-----------+---------------+----------------+--------
x..3o..3o.. ... & | 4 | 6 0 | 4 0 0 | 48 * * * | 1 1 1 0 0 | 2 1 0 tet
xo.3oo. ... ...&#x & | 4 | 3 3 | 1 3 0 | * 192 * * | 0 1 1 1 0 | 1 2 0 tet
xo. ... ox. ...&#x & | 4 | 2 4 | 0 4 0 | * * 72 * | 0 2 0 0 2 | 1 2 1 tet
xoo ... ... ...&#x & | 4 | 1 5 | 0 2 2 | * * * 288 | 0 0 0 1 2 | 0 2 1 tet
------------------------+----+-------+-----------+---------------+----------------+--------
x..3o..3o.. *b3o.. & | 8 | 24 0 | 32 0 0 | 16 0 0 0 | 3 * * * * | 2 0 0 hex
xo.3oo.3ox. ...&#x & | 8 | 12 12 | 8 24 0 | 2 8 6 0 | * 24 * * * | 1 1 0 hex
xo.3oo. ... *b3oo.&#x & | 5 | 6 4 | 4 6 0 | 1 4 0 0 | * * 48 * * | 1 1 0 pen
xoo3ooo ... ...&#x & | 5 | 3 7 | 1 6 3 | 0 2 0 3 | * * * 96 * | 0 2 0 pen
xoo ... oxo ...&#x & | 5 | 2 8 | 0 6 4 | 0 0 1 4 | * * * * 144 | 0 1 1 pen
------------------------+----+-------+-----------+---------------+----------------+--------
xo.3oo.3ox. *b3oo.&#x & | 16 | 48 32 | 64 96 0 | 32 64 24 0 | 2 8 16 0 0 | 3 * * hin
xoo3ooo3oxo ...&#x & | 9 | 12 20 | 8 36 12 | 2 16 6 24 | 0 1 2 8 6 | * 24 * hexpy
xoo ... oxo oox&#x | 6 | 3 12 | 0 12 8 | 0 0 3 12 | 0 0 0 0 6 | * * 24 hix
wendy wrote:It is the tri-diminished 2_21, a creature that i first introduced Richard to the art of lace cities. It's three points shy of a 2_21.
polychoronlover wrote:Today I found that a polypeton could be constructed by taking the convex hull of three hexadecachora in different orientations, each having demitesseractic symmetry, in parallel flunes arranged like the vertices of an equilateral triangle. I think it is scaliform. [...] Here is its lace city:
- Code: Select all
A
/ \
/ \
/ \
B-------C
A = x3o3o *b3o
B = o3o3x *b3o
C = o3o3o *b3x
Has this been found before? Similar shapes can be made from the [...] truncated hexadecachoron [...].
xoo3xxx3oxo *b3oox&#x
o..3o..3o.. *b3o.. & | 144 | 1 4 4 | 4 4 6 8 4 | 4 1 12 2 4 8 4 | 1 4 6 8 5 | 2 5 1
------------------------+-----+------------+--------------------+------------------------+----------------+--------
x.. ... ... ... & | 2 | 72 * * | 4 0 4 0 0 | 4 0 8 2 0 4 0 | 1 4 4 4 4 | 2 4 1
... x.. ... ... & | 2 | * 288 * | 1 2 0 2 0 | 2 1 4 0 2 0 1 | 1 2 4 3 0 | 2 3 0
oo.3oo.3oo. *b3oo.&#x & | 2 | * * 288 | 0 0 2 2 2 | 0 0 4 1 1 5 2 | 0 2 2 5 4 | 1 4 1
------------------------+-----+------------+--------------------+------------------------+----------------+--------
x..3x.. ... ... & | 6 | 3 3 0 | 96 * * * * | 2 0 2 0 0 0 0 | 1 2 2 1 0 | 2 2 0
... x..3o.. ... & | 3 | 0 3 0 | * 192 * * * | 1 1 1 0 1 0 0 | 1 1 3 1 0 | 2 2 0
xo. ... ... ...&#x & | 3 | 1 0 2 | * * 288 * * | 0 0 2 1 0 2 0 | 0 2 1 2 3 | 1 3 1
... xx. ... ...&#x & | 4 | 0 2 2 | * * * 288 * | 0 0 2 0 1 0 1 | 0 1 2 3 0 | 1 3 0
ooo3ooo3ooo *b3ooo&#x | 3 | 0 0 3 | * * * * 192 | 0 0 0 0 0 3 1 | 0 0 0 3 3 | 0 3 1
------------------------+-----+------------+--------------------+------------------------+----------------+--------
x..3x..3o.. ... & | 12 | 6 12 0 | 4 4 0 0 0 | 48 * * * * * * | 1 1 1 0 0 | 2 1 0 tut
... x..3o.. *b3o.. & | 6 | 0 12 0 | 0 8 0 0 0 | * 24 * * * * * | 1 0 2 0 0 | 2 1 0 oct
xo.3xx. ... ...&#x & | 9 | 3 6 6 | 1 1 3 3 0 | * * 192 * * * * | 0 1 1 1 0 | 1 2 0 tricu
xo. ... ox. ...&#x & | 4 | 2 0 4 | 0 0 4 0 0 | * * * 72 * * * | 0 2 0 0 2 | 1 2 1 tet
... xx. ... *b3oo.&#x & | 6 | 0 6 3 | 0 2 0 3 0 | * * * * 96 * * | 0 0 2 1 0 | 1 2 0 trip
xoo ... ... ...&#x & | 4 | 1 0 5 | 0 0 2 0 2 | * * * * * 288 * | 0 0 0 1 2 | 0 2 1 tet
... xxx ... ...&#x | 6 | 0 3 6 | 0 0 0 3 2 | * * * * * * 96 | 0 0 0 3 0 | 0 3 0 trip
------------------------+-----+------------+--------------------+------------------------+----------------+--------
x..3x..3o.. *b3o.. & | 48 | 24 96 0 | 32 64 0 0 0 | 16 8 0 0 0 0 0 | 3 * * * * | 2 0 0 thex
xo.3xx.3ox. ...&#x & | 24 | 12 24 24 | 8 8 24 12 0 | 2 0 8 6 0 0 0 | * 24 * * * | 1 1 0 tutcup
xo.3xx. ... *b3oo.&#x & | 18 | 6 24 12 | 4 12 6 12 0 | 1 1 4 0 4 0 0 | * * 48 * * | 1 1 0 octatut
xoo3xxx ... ...&#x & | 12 | 3 9 15 | 1 2 6 9 6 | 0 0 2 0 1 3 3 | * * * 96 * | 0 2 0 tricuf
xoo ... oxo ...&#x & | 5 | 2 0 8 | 0 0 6 0 4 | 0 0 0 1 0 4 0 | * * * * 144 | 0 1 1 pen
------------------------+-----+------------+--------------------+------------------------+----------------+--------
xo.3xx.3ox. *b3oo.&#x & | 96 | 48 192 96 | 64 128 96 96 0 | 32 16 64 24 32 0 0 | 2 8 16 0 0 | 3 * * thexag thex
xoo3xxx3oxo ...&#x & | 30 | 12 36 48 | 8 16 36 36 24 | 2 1 16 6 8 24 12 | 0 1 2 8 6 | * 24 * octatutcup
xoo ... oxo oox&#x | 6 | 3 0 12 | 0 0 12 0 8 | 0 0 0 3 0 12 0 | 0 0 0 0 6 | * * 24 hix
polychoronlover wrote:... Similar shapes can be made from the rectified tesseract, ..., etc.
xxo3ooo3xox *b3oxx&#x
o..3o..3o.. *b3o.. & | 96 | 6 6 | 6 3 12 18 3 | 3 2 6 18 8 6 15 | 1 8 6 2 7 12 | 2 5 3
------------------------+----+---------+-------------------+--------------------------+-------------------+--------
x.. ... ... ... & | 2 | 288 * | 2 1 2 2 0 | 2 1 2 5 2 1 2 | 1 5 2 1 2 3 | 2 3 1
oo.3oo.3oo. *b3oo.&#x & | 2 | * 288 | 0 0 2 4 1 | 0 0 1 4 2 2 6 | 0 2 2 1 3 6 | 1 3 2
------------------------+----+---------+-------------------+--------------------------+-------------------+--------
x..3o.. ... ... & | 3 | 3 0 | 192 * * * * | 1 1 1 0 1 0 0 | 1 3 0 1 1 0 | 2 2 0
x.. ... x.. ... & | 4 | 4 0 | * 72 * * * | 2 0 0 4 0 0 0 | 1 4 2 0 0 2 | 2 2 1
xx. ... ... ...&#x & | 4 | 2 2 | * * 288 * * | 0 0 1 2 0 0 1 | 0 2 1 0 1 2 | 1 2 1
... ... xo. ...&#x & | 3 | 1 2 | * * * 576 * | 0 0 0 1 1 1 1 | 0 1 1 1 1 2 | 1 2 1
ooo3ooo3ooo *b3ooo&#x | 3 | 0 3 | * * * * 96 | 0 0 0 0 0 0 6 | 0 0 0 0 3 6 | 0 3 2
------------------------+----+---------+-------------------+--------------------------+-------------------+--------
x..3o..3x.. ... & | 12 | 24 0 | 8 6 0 0 0 | 24 * * * * * * | 1 2 0 0 0 0 | 2 1 0 co
x..3o.. ... *b3o.. & | 4 | 6 0 | 4 0 0 0 0 | * 48 * * * * * | 1 1 0 1 0 0 | 2 1 0 tet
xx.3oo. ... ...&#x & | 6 | 6 3 | 2 0 3 0 0 | * * 96 * * * * | 0 2 0 0 1 0 | 1 2 0 trip
xx. ... xo. ...&#x & | 6 | 5 4 | 0 1 2 2 0 | * * * 288 * * * | 0 1 1 0 0 1 | 1 1 1 trip
... oo.3xo. ...&#x & | 4 | 3 3 | 1 0 0 3 0 | * * * * 192 * * | 0 1 0 1 1 0 | 1 2 0 tet
... ... xo. ox.&#x & | 4 | 2 4 | 0 0 0 4 0 | * * * * * 144 * | 0 0 1 1 0 1 | 1 1 1 tet
xxo ... ... ...&#x & | 5 | 2 6 | 0 0 1 2 2 | * * * * * * 288 | 0 0 0 0 1 2 | 0 2 1 squippy
------------------------+----+---------+-------------------+--------------------------+-------------------+--------
x..3o..3x.. *b3o.. & | 32 | 96 0 | 64 24 0 0 0 | 8 16 0 0 0 0 0 | 3 * * * * * | 2 0 0 rit
xx.3oo.3xo. ...&#x & | 16 | 30 12 | 12 6 12 12 0 | 1 1 4 6 4 0 0 | * 48 * * * * | 1 1 0 tetaco
xx. ... xo. ox.&#x & | 8 | 8 8 | 0 2 4 8 0 | 0 0 0 4 0 2 0 | * * 72 * * * | 1 0 1 tepe
... oo.3xo. *b3ox.&#x & | 8 | 12 12 | 8 0 0 24 0 | 0 2 0 0 8 6 0 | * * * 24 * * | 1 1 0 hex
xxo3ooo ... ...&#x & | 7 | 6 9 | 2 0 3 6 3 | 0 0 1 0 2 0 3 | * * * * 96 * | 0 2 0 trippy
xxo ... xox ...&#x & | 8 | 6 12 | 0 1 4 8 4 | 0 0 0 2 0 1 4 | * * * * * 144 | 0 1 1 bidrap
------------------------+----+---------+-------------------+--------------------------+-------------------+--------
xx.3oo.3xo. *b3ox.&#x & | 64 | 192 96 | 128 48 96 192 0 | 16 32 32 96 64 48 0 | 2 16 24 8 0 0 | 3 * * ritag rit
xxo3ooo3xox ...&#x & | 20 | 36 36 | 16 6 24 48 12 | 1 2 8 12 16 6 24 | 0 2 0 1 8 6 | * 24 * coahex
xxo ... xox oxx&#x | 12 | 12 24 | 0 3 12 24 8 | 0 0 0 12 0 6 12 | 0 0 3 0 0 6 | * * 24 tedrix
I thought of a better name for the 6D one, thex gyrotrigonism - thexgyt for short. Trigonism being a fusion of trigon and prism.
The other two could be called ritgyt and tahgyt for short.
xxo3xxx3xox *b3oxx&#x
o..3o..3o.. *b3o.. & | 288 | 2 2 4 | 4 1 1 4 4 6 2 | 2 2 4 6 6 2 5 2 | 1 6 2 2 5 4 | 2 4 1
------------------------+-----+-------------+---------------------------+-----------------------------+-------------------+--------
x.. ... ... ... & | 2 | 288 * * | 2 1 0 2 0 2 0 | 2 1 2 5 2 1 2 0 | 1 5 2 1 2 3 | 2 3 1
... x.. ... ... & | 2 | * 288 * | 2 0 1 0 2 0 0 | 1 2 2 0 4 0 0 1 | 1 4 0 2 3 0 | 2 3 0
oo.3oo.3oo. *b3oo.&#x & | 2 | * * 576 | 0 0 0 1 1 2 1 | 0 0 1 2 2 1 3 1 | 0 2 1 1 3 3 | 1 3 1
------------------------+-----+-------------+---------------------------+-----------------------------+-------------------+--------
x..3x.. ... ... & | 6 | 3 3 0 | 192 * * * * * * | 1 1 1 0 1 0 0 0 | 1 3 0 1 1 0 | 2 2 0
x.. ... x.. ... & | 4 | 4 0 0 | * 72 * * * * * | 2 0 0 4 0 0 0 0 | 1 4 2 0 0 2 | 2 2 1
... x.. ... *b3o.. & | 3 | 0 3 0 | * * 96 * * * * | 0 2 0 0 2 0 0 0 | 1 2 0 2 1 0 | 2 2 0
xx. ... ... ...&#x & | 4 | 2 0 2 | * * * 288 * * * | 0 0 1 2 0 0 1 0 | 0 2 1 0 1 2 | 1 2 1
... xx. ... ...&#x & | 4 | 0 2 2 | * * * * 288 * * | 0 0 1 0 2 0 0 1 | 0 2 0 1 3 0 | 1 3 0
... ... xo. ...&#x & | 3 | 1 0 2 | * * * * * 576 * | 0 0 0 1 1 1 1 0 | 0 1 1 1 1 2 | 1 2 1
ooo3ooo3ooo *b3ooo&#x | 3 | 0 0 3 | * * * * * * 192 | 0 0 0 0 0 0 3 1 | 0 0 0 0 3 3 | 0 3 1
------------------------+-----+-------------+---------------------------+-----------------------------+-------------------+--------
x..3x..3x.. ... & | 24 | 24 12 0 | 8 6 0 0 0 0 0 | 24 * * * * * * * | 1 2 0 0 0 0 | 2 1 0 toe
x..3x.. ... *b3o.. & | 12 | 6 12 0 | 4 0 4 0 0 0 0 | * 48 * * * * * * | 1 1 0 1 0 0 | 2 1 0 tut
xx.3xx. ... ...&#x & | 12 | 6 6 6 | 2 0 0 3 3 0 0 | * * 96 * * * * * | 0 2 0 0 1 0 | 1 2 0 hip
xx. ... xo. ...&#x & | 6 | 5 0 4 | 0 1 0 2 0 2 0 | * * * 288 * * * * | 0 1 1 0 0 1 | 1 1 1 trip
... xx.3xo. ...&#x & | 9 | 3 6 6 | 1 0 1 0 3 3 0 | * * * * 192 * * * | 0 1 0 1 1 0 | 1 2 0 tricu
... ... xo. ox.&#x & | 4 | 2 0 4 | 0 0 0 0 0 4 0 | * * * * * 144 * * | 0 0 1 1 0 1 | 1 1 1 tet
xxo ... ... ...&#x & | 5 | 2 0 6 | 0 0 0 1 0 2 2 | * * * * * * 288 * | 0 0 0 0 1 2 | 0 2 1 squippy
... xxx ... ...&#x | 6 | 0 3 6 | 0 0 0 0 3 0 2 | * * * * * * * 96 | 0 0 0 0 3 0 | 0 3 0 trip
------------------------+-----+-------------+---------------------------+-----------------------------+-------------------+--------
x..3x..3x.. *b3o.. & | 96 | 96 96 0 | 64 24 32 0 0 0 0 | 8 16 0 0 0 0 0 0 | 3 * * * * * | 2 0 0 tah
xx.3xx.3xo. ...&#x & | 36 | 30 24 24 | 12 6 4 12 12 12 0 | 1 1 4 6 4 0 0 0 | * 48 * * * * | 1 1 0 tutatoe
xx. ... xo. ox.&#x & | 8 | 8 0 8 | 0 2 0 4 0 8 0 | 0 0 0 4 0 2 0 0 | * * 72 * * * | 1 0 1 tepe
... xx.3xo. *b3ox.&#x & | 24 | 12 24 24 | 8 0 8 0 12 24 0 | 0 2 0 0 8 6 0 0 | * * * 24 * * | 1 1 0 tutcup
xxo3xxx ... ...&#x & | 15 | 6 9 18 | 2 0 1 3 9 6 6 | 0 0 1 0 2 0 3 3 | * * * * 96 * | 0 2 0 tripuf
xxo ... xox ...&#x & | 8 | 6 0 12 | 0 1 0 4 0 8 4 | 0 0 0 2 0 1 4 0 | * * * * * 144 | 0 1 1 bidrap
------------------------+-----+-------------+---------------------------+-----------------------------+-------------------+--------
xx.3xx.3xo. *b3ox.&#x & | 192 | 192 192 192 | 128 48 64 96 96 192 0 | 16 32 32 96 64 48 0 0 | 2 16 24 8 0 0 | 3 * * tahagtah
xxo3xxx3xox ...&#x & | 48 | 36 36 72 | 16 6 8 24 36 48 24 | 1 2 8 12 16 6 24 12 | 0 2 0 1 8 6 | * 24 * toa tutcup
xxo ... xox oxx&#x | 12 | 12 0 24 | 0 3 0 12 0 24 8 | 0 0 0 12 0 6 12 0 | 0 0 3 0 0 6 | * * 24 tedrix
polychoronlover wrote:I was thinking "thex-cupolitrigonism" for thexgyt, or "thex-cupolitrism" for short, similar to the truncated tetrahedral cupoliprism, to represent lace towers of the same shape in different orientations.
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