snub demipenteract,
alternation of great prismated triacontaditeron
- general polytopal classes:
- isogonal
links
| Acronym | snippit (old: spitac, alt.: snahin) |
| Name |
snub prismatotriacontaditeron, snub demipenteract, alternation of great prismated triacontaditeron |
| Circumradius | ... |
| Face vector | 960, 6720, 10880, 6240, 1122 |
| Confer |
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External links |
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This isogonal polyteron is obtained by hemiation of gippit. But because of lower degree of freedom the resulting edge sizes cannot be made all alike.
Snippit is meant to be used for all variations under the full symmetry, i.e. for s3s3s3s4o. Snahin is meant to be used for all subsymmetric variations, i.e. for s3s3s *b3s3s.
Incidence matrix according to Dynkin symbol
s3s3s3s4o
demi( . . . . . ) | 960 | 1 2 2 1 2 2 4 | 1 1 2 3 6 6 3 6 3 3 | 1 2 2 1 2 1 1 8 4 4 4 | 2 1 1 1 5
------------------+-----+------------------------------+--------------------------------------------+--------------------------------------------+----------------
s 2 s . . | 2 | 480 * * * * * * | 0 0 0 2 0 4 0 0 0 0 | 1 0 2 0 0 0 0 4 0 2 0 | 2 0 1 0 2 q
s 2 . s . | 2 | * 960 * * * * * | 0 0 0 0 2 2 2 0 0 0 | 0 1 1 1 0 0 0 2 2 2 0 | 1 1 1 0 2 q
. s 2 s . | 2 | * * 960 * * * * | 0 0 0 0 2 0 0 2 2 0 | 0 1 0 0 1 1 0 2 2 0 2 | 1 1 0 1 2 q
. . . s4o | 2 | * * * 480 * * * | 0 0 0 0 0 0 2 0 2 2 | 0 0 0 1 0 1 1 0 2 2 2 | 0 1 1 1 2 q
sefa( s3s . . . ) | 2 | * * * * 960 * * | 1 0 0 1 2 0 0 0 0 0 | 1 2 0 0 0 0 0 2 1 0 0 | 2 1 0 0 1 h
sefa( . s3s . . ) | 2 | * * * * * 960 * | 0 1 0 1 0 0 0 2 0 0 | 1 0 0 0 2 0 0 2 0 0 1 | 2 0 0 1 1 h
sefa( . . s3s . ) | 2 | * * * * * * 1920 | 0 0 1 0 0 1 0 1 0 1 | 0 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1 h
------------------+-----+------------------------------+--------------------------------------------+--------------------------------------------+----------------
s3s . . . | 3 | 0 0 0 0 3 0 0 | 320 * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 0 | 2 1 0 0 0 h3o
. s3s . . | 3 | 0 0 0 0 0 3 0 | * 320 * * * * * * * * | 1 0 0 0 2 0 0 0 0 0 0 | 2 0 0 1 0 h3o
. . s3s . | 3 | 0 0 0 0 0 0 3 | * * 640 * * * * * * * | 0 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0 h3o
sefa( s3s3s . . ) | 3 | 1 0 0 0 1 1 0 | * * * 960 * * * * * * | 1 0 0 0 0 0 0 2 0 0 0 | 2 0 0 0 1 oq&#h
sefa( s3s 2 s . ) | 3 | 0 1 1 0 1 0 0 | * * * * 1920 * * * * * | 0 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 oh&#q
sefa( s 2 s3s . ) | 3 | 1 1 0 0 0 0 1 | * * * * * 1920 * * * * | 0 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 oh&#q
sefa( s 2 . s4o ) | 3 | 0 2 0 1 0 0 0 | * * * * * * 960 * * * | 0 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 q3o
sefa( . s3s3s . ) | 3 | 0 0 1 0 0 1 1 | * * * * * * * 1920 * * | 0 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 oq&#h
sefa( . s 2 s4o ) | 3 | 0 0 2 1 0 0 0 | * * * * * * * * 960 * | 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 q3o
sefa( . . s3s4o ) | 3 | 0 0 0 1 0 0 2 | * * * * * * * * * 960 | 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 oq&#h
------------------+-----+------------------------------+--------------------------------------------+--------------------------------------------+----------------
s3s3s . . | 12 | 6 0 0 0 12 12 0 | 4 4 0 12 0 0 0 0 0 0 | 80 * * * * * * * * * * | 2 0 0 0 0 pyritohedral ike variant
s3s 2 s . | 6 | 0 3 3 0 6 0 0 | 2 0 0 0 6 0 0 0 0 0 | * 320 * * * * * * * * * | 1 1 0 0 0 triangular antiprism
s 2 s3s . | 6 | 3 3 0 0 0 0 6 | 0 0 2 0 0 6 0 0 0 0 | * * 320 * * * * * * * * | 1 0 1 0 0 triangular antiprism
s 2 . s4o | 4 | 0 4 0 2 0 0 0 | 0 0 0 0 0 0 4 0 0 0 | * * * 240 * * * * * * * | 0 1 1 0 0 q-tetrahedra
. s3s3s . | 12 | 0 0 6 0 0 12 12 | 0 4 4 0 0 0 0 12 0 0 | * * * * 160 * * * * * * | 1 0 0 1 0 pyritohedral ike variant
. s 2 s4o | 4 | 0 0 4 2 0 0 0 | 0 0 0 0 0 0 0 0 4 0 | * * * * * 240 * * * * * | 0 1 0 1 0 q-tetrahedra
. . s3s4o | 12 | 0 0 0 6 0 0 24 | 0 0 8 0 0 0 0 0 0 12 | * * * * * * 80 * * * * | 0 0 1 1 0 pyritohedral ike variant
sefa( s3s3s3s . ) | 4 | 1 1 1 0 1 1 1 | 0 0 0 1 1 1 0 1 0 0 | * * * * * * * 1920 * * * | 1 0 0 0 1 chiral digonal antifrustrum (disphenoid)
sefa( s3s 2 s4o ) | 4 | 0 2 2 1 1 0 0 | 0 0 0 0 2 0 1 0 1 0 | * * * * * * * * 960 * * | 0 1 0 0 1 symmetric digonal antifrustrum (disphenoid)
sefa( s 2 s3s4o ) | 4 | 1 2 0 1 0 0 2 | 0 0 0 0 0 2 1 0 0 1 | * * * * * * * * * 960 * | 0 0 1 0 1 pyramid above isot
sefa( . s3s3s4o ) | 4 | 0 0 2 1 0 1 2 | 0 0 0 0 0 0 0 2 1 1 | * * * * * * * * * * 960 | 0 0 0 1 1 trigonal pyramid
------------------+-----+------------------------------+--------------------------------------------+--------------------------------------------+----------------
s3s3s3s . | 60 | 30 30 30 0 60 60 60 | 20 20 20 60 60 60 0 60 0 0 | 5 10 10 0 5 0 0 60 0 0 0 | 32 * * * * snub decachoron
s3s 2 s4o | 12 | 0 12 12 6 12 0 0 | 4 0 0 0 24 0 12 0 12 0 | 0 4 0 3 0 3 0 0 12 0 0 | * 80 * * * 2-3-duoantiprism
s 2 s3s4o | 24 | 12 24 0 12 0 0 48 | 0 0 16 0 0 48 24 0 0 24 | 0 0 8 6 0 0 2 0 0 24 0 | * * 40 * * pyritohedral ike antiprism
. s3s3s4o | 96 | 0 0 96 48 0 96 192 | 0 32 64 0 0 0 0 192 96 96 | 0 0 0 0 16 24 8 0 0 0 96 | * * * 10 * pyritohedral sadi variant
sefa( s3s3s3s4o ) | 5 | 1 2 2 1 1 1 2 | 0 0 0 1 2 2 1 2 1 1 | 0 0 0 0 0 0 0 2 1 1 1 | * * * * 960 pentachoron variant
starting figure: x3x3x3x4o
s
3 \
s---s---s
3 / 3 3
s
s3s3s *b3s3s
demi( . . . . . ) | 960 | 1 1 1 1 1 1 2 2 2 2 | 1 1 1 1 3 3 3 3 3 3 3 3 3 3 | 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 | 1 1 1 1 1 5
---------------------+-----+-----------------------------------------+---------------------------------------------------------+---------------------------------------------------------+-------------------
s 2 s . . | 2 | 480 * * * * * * * * * | 0 0 0 0 2 0 0 2 2 0 0 0 0 0 | 1 0 0 1 1 0 0 0 0 0 2 2 0 2 0 | 1 1 0 1 0 2
s . 2 s . | 2 | * 480 * * * * * * * * | 0 0 0 0 0 2 0 2 0 2 0 0 0 0 | 0 1 0 1 0 1 0 0 0 0 2 0 2 2 0 | 1 0 1 1 0 2
s . 2 . s | 2 | * * 480 * * * * * * * | 0 0 0 0 0 0 2 0 2 2 0 0 0 0 | 0 0 1 0 1 1 0 0 0 0 0 2 2 2 0 | 0 1 1 1 0 2
. s . 2 s | 2 | * * * 480 * * * * * * | 0 0 0 0 0 0 2 0 0 0 0 2 2 0 | 0 0 1 0 0 0 0 1 1 0 0 2 2 0 2 | 0 1 1 0 1 2
. . s 2 s . | 2 | * * * * 480 * * * * * | 0 0 0 0 0 0 0 2 0 0 2 0 0 2 | 0 0 0 1 0 0 1 0 0 1 2 0 0 2 2 | 1 0 0 1 1 2
. . s 2 . s | 2 | * * * * * 480 * * * * | 0 0 0 0 0 0 0 0 2 0 0 2 0 2 | 0 0 0 0 1 0 0 1 0 1 0 2 0 2 2 | 0 1 0 1 1 2
sefa( s3s . . . ) | 2 | * * * * * * 960 * * * | 1 0 0 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1
sefa( . s3s . . ) | 2 | * * * * * * * 960 * * | 0 1 0 0 1 0 0 0 0 0 1 1 0 0 | 1 0 0 0 0 0 1 1 0 0 1 1 0 0 1 | 1 1 0 0 1 1
sefa( . s . *b3s . ) | 2 | * * * * * * * * 960 * | 0 0 1 0 0 1 0 0 0 0 1 0 1 0 | 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 | 1 0 1 0 1 1
sefa( . . . s3s ) | 2 | * * * * * * * * * 960 | 0 0 0 1 0 0 0 0 0 1 0 0 1 1 | 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
---------------------+-----+-----------------------------------------+---------------------------------------------------------+---------------------------------------------------------+-------------------
s3s . . . | 3 | 0 0 0 0 0 0 3 0 0 0 | 320 * * * * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 h3o
. s3s . . | 3 | 0 0 0 0 0 0 0 3 0 0 | * 320 * * * * * * * * * * * * | 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 | 1 1 0 0 1 0 h3o
. s . *b3s . | 3 | 0 0 0 0 0 0 0 0 3 0 | * * 320 * * * * * * * * * * * | 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 | 1 0 1 0 1 0 h3o
. . . s3s | 3 | 0 0 0 0 0 0 0 0 0 3 | * * * 320 * * * * * * * * * * | 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0 h3o
sefa( s3s3s . . ) | 3 | 1 0 0 0 0 0 1 1 0 0 | * * * * 960 * * * * * * * * * | 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1 oq&#h
sefa( s3s . *b3s . ) | 3 | 0 1 0 0 0 0 1 0 1 0 | * * * * * 960 * * * * * * * * | 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1 oq&#h
sefa( s3s 2 . s ) | 3 | 0 0 1 1 0 0 1 0 0 0 | * * * * * * 960 * * * * * * * | 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1 oh&#q
sefa( s 2 s 2 s . ) | 3 | 1 1 0 0 1 0 0 0 0 0 | * * * * * * * 960 * * * * * * | 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1 q3o
sefa( s 2 s 2 . s ) | 3 | 1 0 1 0 0 1 0 0 0 0 | * * * * * * * * 960 * * * * * | 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 | 0 1 0 1 0 1 q3o
sefa( s . 2 s3s ) | 3 | 0 1 1 0 0 0 0 0 0 1 | * * * * * * * * * 960 * * * * | 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1 oh&#q
sefa( . s3s *b3s . ) | 3 | 0 0 0 0 1 0 0 1 1 0 | * * * * * * * * * * 960 * * * | 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 | 1 0 0 0 1 1 oq&#h
sefa( . s3s 2 . s ) | 3 | 0 0 0 1 0 1 0 1 0 0 | * * * * * * * * * * * 960 * * | 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1 oh&#q
sefa( . s . *b3s3s ) | 3 | 0 0 0 1 0 0 0 0 1 1 | * * * * * * * * * * * * 960 * | 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1 oq&#h
sefa( . . s 2 s3s ) | 3 | 0 0 0 0 1 1 0 0 0 1 | * * * * * * * * * * * * * 960 | 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1 oh&#q
---------------------+-----+-----------------------------------------+---------------------------------------------------------+---------------------------------------------------------+-------------------
s3s3s . . | 12 | 6 0 0 0 0 0 12 12 0 0 | 4 4 0 0 12 0 0 0 0 0 0 0 0 0 | 80 * * * * * * * * * * * * * * | 1 1 0 0 0 0 pyritohedral ike variant
s3s . *b3s . | 12 | 0 6 0 0 0 0 12 0 12 0 | 4 0 4 0 0 12 0 0 0 0 0 0 0 0 | * 80 * * * * * * * * * * * * * | 1 0 1 0 0 0 pyritohedral ike variant
s3s 2 . s | 6 | 0 0 3 3 0 0 6 0 0 0 | 2 0 0 0 0 0 6 0 0 0 0 0 0 0 | * * 160 * * * * * * * * * * * * | 0 1 1 0 0 0 triangular antiprism
s 2 s 2 s . | 4 | 2 2 0 0 2 0 0 0 0 0 | 0 0 0 0 0 0 0 4 0 0 0 0 0 0 | * * * 240 * * * * * * * * * * * | 1 0 0 1 0 0 q-tetrahedra
s 2 s 2 . s | 4 | 2 0 2 0 0 2 0 0 0 0 | 0 0 0 0 0 0 0 0 4 0 0 0 0 0 | * * * * 240 * * * * * * * * * * | 0 1 0 1 0 0 q-tetrahedra
s . 2 s3s | 6 | 0 3 3 0 0 0 0 0 0 6 | 0 0 0 2 0 0 0 0 0 6 0 0 0 0 | * * * * * 160 * * * * * * * * * | 0 0 1 1 0 0 triangular antiprism
. s3s *b3s . | 12 | 0 0 0 0 6 0 0 12 12 0 | 0 4 4 0 0 0 0 0 0 0 12 0 0 0 | * * * * * * 80 * * * * * * * * | 1 0 0 0 1 0 pyritohedral ike variant
. s3s 2 . s | 6 | 0 0 0 3 0 3 0 6 0 0 | 0 2 0 0 0 0 0 0 0 0 0 6 0 0 | * * * * * * * 160 * * * * * * * | 0 1 0 0 1 0 triangular antiprism
. s . *b3s3s | 12 | 0 0 0 6 0 0 0 0 12 12 | 0 0 4 4 0 0 0 0 0 0 0 0 12 0 | * * * * * * * * 80 * * * * * * | 0 0 1 0 1 0 pyritohedral ike variant
. . s 2 s3s | 6 | 0 0 0 0 3 3 0 0 0 6 | 0 0 0 2 0 0 0 0 0 0 0 0 0 6 | * * * * * * * * * 160 * * * * * | 0 0 0 1 1 0 triangular antiprism
sefa( s3s3s *c3s . ) | 4 | 1 1 0 0 1 0 1 1 1 0 | 0 0 0 0 1 1 0 1 0 0 1 0 0 0 | * * * * * * * * * * 960 * * * * | 1 0 0 0 0 1 trigonal pyramid
sefa( s3s3s 2 s ) | 4 | 1 0 1 1 0 1 1 1 0 0 | 0 0 0 0 1 0 1 0 1 0 0 1 0 0 | * * * * * * * * * * * 960 * * * | 0 1 0 0 0 1 pyramid above isot
sefa( s3s . *c3s3s ) | 4 | 0 1 1 1 0 0 1 0 1 1 | 0 0 0 0 0 1 1 0 0 1 0 0 1 0 | * * * * * * * * * * * * 960 * * | 0 0 1 0 0 1 chiral digonal antifrustrum (disphenoid)
sefa( s 2 s 2 s3s ) | 4 | 1 1 1 0 1 1 0 0 0 1 | 0 0 0 0 0 0 0 1 1 1 0 0 0 1 | * * * * * * * * * * * * * 960 * | 0 0 0 1 0 1 symmetric digonal antifrustrum (disphenoid)
sefa( . s3s *c3s3s ) | 4 | 0 0 0 1 1 1 0 1 1 1 | 0 0 0 0 0 0 0 0 0 0 1 1 1 1 | * * * * * * * * * * * * * * 960 | 0 0 0 0 1 1 chiral digonal antifrustrum (disphenoid)
---------------------+-----+-----------------------------------------+---------------------------------------------------------+---------------------------------------------------------+-------------------
s3s3s *c3s . | 96 | 48 48 0 0 48 0 96 96 96 0 | 32 32 32 0 96 96 0 96 0 0 96 0 0 0 | 8 8 0 24 0 0 8 0 0 0 96 0 0 0 0 | 10 * * * * * pyritohedral sadi variant
s3s3s 2 s | 24 | 12 0 12 12 0 12 24 24 0 0 | 8 8 0 0 24 0 24 0 24 0 0 24 0 0 | 2 0 4 0 6 0 0 4 0 0 0 24 0 0 0 | * 40 * * * * pyritohedral ike antiprism
s3s . *c3s3s | 60 | 0 30 30 30 0 0 60 0 60 60 | 20 0 20 20 0 60 60 0 0 60 0 0 60 0 | 0 5 10 0 0 10 0 0 5 0 0 0 60 0 0 | * * 16 * * * snub decachoron
s 2 s 2 s3s | 12 | 6 6 6 0 6 6 0 0 0 12 | 0 0 0 4 0 0 0 12 12 12 0 0 0 12 | 0 0 0 3 3 2 0 0 0 2 0 0 0 12 0 | * * * 80 * * 2-3-duoantiprism
. s3s *c3s3s | 60 | 0 0 0 30 30 30 0 60 60 60 | 0 20 20 20 0 0 0 0 0 0 60 60 60 60 | 0 0 0 0 0 0 5 10 5 10 0 0 0 0 60 | * * * * 16 * snub decachoron
sefa( s3s3s *b3s3s ) | 5 | 1 1 1 1 1 1 1 1 1 1 | 0 0 0 0 1 1 1 1 1 1 1 1 1 1 | 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 | * * * * * 960 pentachoron variant
starting figure: x3x3x *b3x3x
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