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Acronym
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hext
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Name
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hexadecachoric tetracomb,
demitesseractic tetracomb,
Delone complex of body-centered tesseractic lattice,
Gosset polytope 11,1,1
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Vertex layers
(first ones only)
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Coordinates
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-
-
(i, j, k, l) i.e. all integer touples
(inscribed test) and
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(i+1/2, j+1/2, k+1/2, l+1/2) i.e. all half-integer touples
(its body centers, a shifted test)
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or just (i/sqrt(2), j/sqrt(2), k/sqrt(2), l/sqrt(2)) for integers i,j,k,l with i+j+k+l even
(as being the hemiation of test)
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Dual
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icot
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Confer
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- related tesselations:
-
Delone complex of primitive tesseractic lattice
Voronoi complex of primitive tesseractic lattice
Voronoi complex of bct lattice
- ambification:
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icot
- general polytopal classes:
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noble polytopes
partial Stott expansions
Coxeter-Elte-Gosset polytopes
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External
links
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Incidence matrix according to Dynkin symbol
x3o3o4o3o (N → ∞)
. . . . . | N ♦ 24 | 96 | 96 | 24
----------+---+-----+-----+-----+---
x . . . . | 2 | 12N ♦ 8 | 12 | 6
----------+---+-----+-----+-----+---
x3o . . . | 3 | 3 | 32N | 3 | 3
----------+---+-----+-----+-----+---
x3o3o . . ♦ 4 | 6 | 4 | 24N | 2
----------+---+-----+-----+-----+---
x3o3o4o . ♦ 8 | 24 | 32 | 16 | 3N
x3o3o *b3o4o (N → ∞)
. . . . . | N ♦ 24 | 96 | 32 64 | 16 8
-------------+---+-----+-----+--------+-----
x . . . . | 2 | 12N ♦ 8 | 4 8 | 4 2
-------------+---+-----+-----+--------+-----
x3o . . . | 3 | 3 | 32N | 1 2 | 2 1
-------------+---+-----+-----+--------+-----
x3o3o . . ♦ 4 | 6 | 4 | 8N * | 2 0
x3o . *b3o . ♦ 4 | 6 | 4 | * 16N | 1 1
-------------+---+-----+-----+--------+-----
x3o3o *b3o . ♦ 8 | 24 | 32 | 8 8 | 2N *
x3o . *b3o4o ♦ 8 | 24 | 32 | 0 16 | * N
x3o3o *b3o *b3o (N → ∞)
. . . . . | N ♦ 24 | 96 | 32 32 32 | 8 8 8
----------------+---+-----+-----+----------+------
x . . . . | 2 | 12N ♦ 8 | 4 4 4 | 2 2 2
----------------+---+-----+-----+----------+------
x3o . . . | 3 | 3 | 32N | 1 1 1 | 1 1 1
----------------+---+-----+-----+----------+------
x3o3o . . ♦ 4 | 6 | 4 | 8N * * | 1 1 0
x3o . *b3o . ♦ 4 | 6 | 4 | * 8N * | 1 0 1
x3o . . *b3o ♦ 4 | 6 | 4 | * * 8N | 0 1 1
----------------+---+-----+-----+----------+------
x3o3o *b3o . ♦ 8 | 24 | 32 | 8 8 0 | N * *
x3o3o . *b3o ♦ 8 | 24 | 32 | 8 0 8 | * N *
x3o . *b3o *b3o ♦ 8 | 24 | 32 | 0 8 8 | * * N
s4o3o3o4o (N → ∞)
demi( . . . . . ) | N ♦ 24 | 96 | 32 64 | 16 8
------------------+---+-----+-----+--------+-----
s4o . . . | 2 | 12N ♦ 8 | 4 8 | 4 2
------------------+---+-----+-----+--------+-----
sefa( s4o3o . . ) | 3 | 3 | 32N | 1 2 | 2 1
------------------+---+-----+-----+--------+-----
s4o3o . . ♦ 4 | 6 | 4 | 8N * | 2 0
sefa( s4o3o3o . ) ♦ 4 | 6 | 4 | * 16N | 1 1
------------------+---+-----+-----+--------+-----
s4o3o3o . ♦ 8 | 24 | 32 | 8 8 | 2N *
sefa( s4o3o3o4o ) ♦ 8 | 24 | 32 | 0 16 | * N
starting figure: x4o3o3o4o
s4o3o3o4s (N → ∞)
demi( . . . . . ) | 8N ♦ 6 12 6 | 12 36 36 12 | 4 12 12 4 4 16 24 16 4 | 1 4 6 4 1 8
------------------+----+-------------+-----------------+---------------------------------+----------------
s4o . . . | 2 | 24N * * ♦ 4 4 0 0 | 2 2 0 0 2 4 2 0 0 | 1 2 1 0 0 2
s . 2 . s | 2 | * 48N * ♦ 0 4 4 0 | 0 2 2 0 0 2 4 2 0 | 0 1 2 1 0 2
. . . o4s | 2 | * * 24N ♦ 0 0 4 4 | 0 0 2 2 0 0 2 4 2 | 0 0 1 2 1 2
------------------+----+-------------+-----------------+---------------------------------+----------------
sefa( s4o3o . . ) | 3 | 3 0 0 | 32N * * * | 1 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
sefa( s4o . 2 s ) | 3 | 1 2 0 | * 96N * * | 0 1 0 0 0 1 1 0 0 | 0 1 1 0 0 1
sefa( s 2 . o4s ) | 3 | 0 2 1 | * * 96N * | 0 0 1 0 0 0 1 1 0 | 0 0 1 1 0 1
sefa( . . o3o4s ) | 3 | 0 0 3 | * * * 32N | 0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
------------------+----+-------------+-----------------+---------------------------------+----------------
s4o3o . . ♦ 4 | 6 0 0 | 4 0 0 0 | 8N * * * * * * * * | 1 1 0 0 0 0
s4o . 2 s ♦ 4 | 2 4 0 | 0 4 0 0 | * 24N * * * * * * * | 0 1 1 0 0 0
s 2 . o4s ♦ 4 | 0 4 2 | 0 0 4 0 | * * 24N * * * * * * | 0 0 1 1 0 0
. . o3o4s ♦ 4 | 0 0 6 | 0 0 0 4 | * * * 8N * * * * * | 0 0 0 1 1 0
sefa( s4o3o3o . ) ♦ 4 | 6 0 0 | 4 0 0 0 | * * * * 8N * * * * | 1 0 0 0 0 1
sefa( s4o3o 2 s ) ♦ 4 | 3 3 0 | 1 3 0 0 | * * * * * 32N * * * | 0 1 0 0 0 1
sefa( s4o 2 o4s ) ♦ 4 | 1 4 1 | 0 2 2 0 | * * * * * * 48N * * | 0 0 1 0 0 1
sefa( s 2 o3o4s ) ♦ 4 | 0 3 3 | 0 0 3 1 | * * * * * * * 32N * | 0 0 0 1 0 1
sefa( . o3o3o4s ) ♦ 4 | 0 0 6 | 0 0 0 4 | * * * * * * * * 8N | 0 0 0 0 1 1
------------------+----+-------------+-----------------+---------------------------------+----------------
s4o3o3o . ♦ 8 | 24 0 0 | 32 0 0 0 | 8 0 0 0 8 0 0 0 0 | N * * * * *
s4o3o 2 s ♦ 8 | 12 12 0 | 8 24 0 0 | 2 6 0 0 0 8 0 0 0 | * 4N * * * *
s4o 2 o4s ♦ 8 | 4 16 4 | 0 16 16 0 | 0 4 4 0 0 0 8 0 0 | * * 6N * * *
s 2 o3o4s ♦ 8 | 0 12 12 | 0 0 24 8 | 0 0 6 2 0 0 0 8 0 | * * * 4N * *
. o3o3o4s ♦ 8 | 0 0 24 | 0 0 0 32 | 0 0 0 8 0 0 0 0 8 | * * * * N *
sefa( s4o3o3o4s ) ♦ 8 | 6 12 6 | 4 12 12 4 | 0 0 0 0 1 4 6 4 1 | * * * * * 8N
starting figure: x4o3o3o4x