Acronym | icot |
Name |
icositetrachoric tetracomb, Voronoi complex of body-centered tesseractic (bct) lattice, Gosset polytope 01,1,1,1 |
Coordinates | |
Dual | hext |
Confer |
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External links |
Incidence matrix according to Dynkin symbol
x3o4o3o3o (N → ∞) . . . . . | 3N ♦ 16 | 32 | 24 | 8 ----------+----+-----+-----+-----+-- x . . . . | 2 | 24N ♦ 4 | 6 | 4 ----------+----+-----+-----+-----+-- x3o . . . | 3 | 3 | 32N | 3 | 3 ----------+----+-----+-----+-----+-- x3o4o . . ♦ 6 | 12 | 8 | 12N | 2 ----------+----+-----+-----+-----+-- x3o4o3o . ♦ 24 | 96 | 96 | 24 | N
o3o4o3x3o (N → ∞) . . . . . | 12N ♦ 16 | 24 8 | 12 12 | 2 6 ----------+-----+-----+---------+---------+----- . . . x . | 2 | 96N ♦ 3 1 | 3 3 | 1 3 ----------+-----+-----+---------+---------+----- . . o3x . | 3 | 3 | 96N * | 2 1 | 1 2 . . . x3o | 3 | 3 | * 32N | 0 3 | 0 3 ----------+-----+-----+---------+---------+----- . o4o3x . ♦ 6 | 12 | 8 0 | 24N * | 1 1 . . o3x3o ♦ 6 | 12 | 4 4 | * 24N | 0 2 ----------+-----+-----+---------+---------+----- o3o4o3x . ♦ 24 | 96 | 96 0 | 24 0 | N * . o4o3x3o ♦ 24 | 96 | 64 32 | 8 16 | * 3N
o4o3x3o4o (N → ∞) . . . . . | 6N ♦ 16 | 16 16 | 4 16 4 | 4 4 ----------+----+-----+---------+-----------+---- . . x . . | 2 | 48N ♦ 2 2 | 1 4 1 | 2 2 ----------+----+-----+---------+-----------+---- . o3x . . | 3 | 3 | 32N * | 1 2 0 | 2 1 . . x3o . | 3 | 3 | * 32N | 0 2 1 | 1 2 ----------+----+-----+---------+-----------+---- o4o3x . . ♦ 6 | 12 | 8 0 | 4N * * | 2 0 . o3x3o . ♦ 6 | 12 | 4 4 | * 16N * | 1 1 . . x3o4o ♦ 6 | 12 | 0 8 | * * 4N | 0 2 ----------+----+-----+---------+-----------+---- o4o3x3o . ♦ 24 | 96 | 64 32 | 8 16 0 | N * . o3x3o4o ♦ 24 | 96 | 32 64 | 0 16 8 | * N
or . . . . . | 3N ♦ 16 | 32 | 8 16 | 8 -------------+----+-----+-----+-------+-- . . x . . | 2 | 24N ♦ 4 | 2 4 | 4 -------------+----+-----+-----+-------+-- . o3x . . & | 3 | 3 | 32N | 1 2 | 3 -------------+----+-----+-----+-------+-- o4o3x . . & ♦ 6 | 12 | 8 | 4N * | 2 . o3x3o . ♦ 6 | 12 | 8 | * 8N | 2 -------------+----+-----+-----+-------+-- o4o3x3o . & ♦ 24 | 96 | 96 | 8 16 | N
o3x3o *b3o4o (N → ∞) . . . . . | 12N ♦ 16 | 8 8 16 | 4 8 8 4 | 4 2 2 -------------+-----+-----+-------------+---------------+------- . x . . . | 2 | 96N ♦ 1 1 2 | 1 2 2 1 | 2 1 1 -------------+-----+-----+-------------+---------------+------- o3x . . . | 3 | 3 | 32N * * | 1 2 0 0 | 2 1 0 . x3o . . | 3 | 3 | * 32N * | 1 0 2 0 | 2 0 1 . x . *b3o . | 3 | 3 | * * 64N | 0 1 1 1 | 1 1 1 -------------+-----+-----+-------------+---------------+------- o3x3o . . ♦ 6 | 12 | 4 4 0 | 8N * * * | 2 0 0 o3x . *b3o . ♦ 6 | 12 | 4 0 4 | * 16N * * | 1 1 0 . x3o *b3o . ♦ 6 | 12 | 0 4 4 | * * 16N * | 1 0 1 . x . *b3o4o ♦ 6 | 12 | 0 0 8 | * * * 8N | 0 1 1 -------------+-----+-----+-------------+---------------+------- o3x3o *b3o . ♦ 24 | 96 | 32 32 32 | 8 8 8 0 | 2N * * o3x . *b3o4o ♦ 24 | 96 | 32 0 64 | 0 16 0 8 | * N * . x3o *b3o4o ♦ 24 | 96 | 0 32 64 | 0 0 16 8 | * * N
o3x3o *b3o *b3o (N → ∞) . . . . . | 12N ♦ 16 | 8 8 8 8 | 4 4 4 4 4 4 | 2 2 2 2 ----------------+-----+-----+-----------------+-------------------+-------- . x . . . | 2 | 96N ♦ 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1 ----------------+-----+-----+-----------------+-------------------+-------- o3x . . . | 3 | 3 | 32N * * * | 1 1 1 0 0 0 | 1 1 1 0 . x3o . . | 3 | 3 | * 32N * * | 1 0 0 1 1 0 | 1 1 0 1 . x . *b3o . | 3 | 3 | * * 32N * | 0 1 0 1 0 1 | 1 0 1 1 . x . . *b3o | 3 | 3 | * * * 32N | 0 0 1 0 1 1 | 0 1 1 1 ----------------+-----+-----+-----------------+-------------------+-------- o3x3o . . ♦ 6 | 12 | 4 4 0 0 | 8N * * * * * | 1 1 0 0 o3x . *b3o . ♦ 6 | 12 | 4 0 4 0 | * 8N * * * * | 1 0 1 0 o3x . . *b3o ♦ 6 | 12 | 4 0 0 4 | * * 8N * * * | 0 1 1 0 . x3o *b3o . ♦ 6 | 12 | 0 4 4 0 | * * * 8N * * | 1 0 0 1 . x3o . *b3o ♦ 6 | 12 | 0 4 0 4 | * * * * 8N * | 0 1 0 1 . x . *b3o *b3o ♦ 6 | 12 | 0 0 4 4 | * * * * * 8N | 0 0 1 1 ----------------+-----+-----+-----------------+-------------------+-------- o3x3o *b3o . ♦ 24 | 96 | 32 32 32 0 | 8 8 0 8 0 0 | N * * * o3x3o . *b3o ♦ 24 | 96 | 32 32 0 32 | 8 0 8 0 8 0 | * N * * o3x . *b3o *b3o ♦ 24 | 96 | 32 0 32 32 | 0 8 8 0 0 8 | * * N * . x3o *b3o *b3o ♦ 24 | 96 | 0 32 32 32 | 0 0 0 8 8 8 | * * * N
:oo:4:xo:3:ox:4:oo:&##x (N → ∞) → height = 1/sqrt(2) = 0.707107 o. 4 o. 3 o. 4 o. | 3N * ♦ 8 4 0 4 | 8 8 4 0 8 4 | 2 4 8 0 8 2 | 4 4 .o 4 .o 3 .o 4 .o | * 3N ♦ 0 4 8 4 | 0 4 8 8 4 8 | 0 2 8 2 8 4 | 4 4 ------------------------+-------+-----------------+-----------------------+-----------------+---- .. x. .. .. | 2 0 | 12N * * * ♦ 2 1 0 0 1 0 | 1 1 2 0 2 0 | 2 2 oo 4 oo 3 oo 4 oo &#x | 1 1 | * 12N * * ♦ 0 2 2 0 0 0 | 0 1 4 0 0 1 | 2 2 .. .. .x .. | 0 2 | * * 12N * ♦ 0 0 1 2 0 1 | 0 0 2 1 2 1 | 2 2 :oo:4:oo:3:oo:4:oo:&#x | 1 1 | * * * 12N ♦ 0 0 0 0 2 2 | 0 1 0 0 4 1 | 2 2 ------------------------+-------+-----------------+-----------------------+-----------------+---- .. x. 3 o. .. | 3 0 | 3 0 0 0 | 8N * * * * * | 1 0 1 0 1 0 | 1 2 .. xo .. .. &#x | 2 1 | 1 2 0 0 | * 12N * * * * | 0 1 2 0 0 0 | 2 1 .. .. ox .. &#x | 1 2 | 0 2 1 0 | * * 12N * * * | 0 0 2 0 0 1 | 1 2 .. .o 3 .x .. | 0 3 | 0 0 3 0 | * * * 8N * * | 0 0 1 1 1 0 | 2 1 .. :xo: .. .. &#x | 2 1 | 1 0 0 2 | * * * * 12N * | 0 1 0 0 2 0 | 2 1 .. .. :ox: .. &#x | 1 2 | 0 0 1 2 | * * * * * 12N | 0 0 0 0 2 1 | 1 2 ------------------------+-------+-----------------+-----------------------+-----------------+---- .. x. 3 o. 4 o. ♦ 6 0 | 12 0 0 0 | 8 0 0 0 0 0 | N * * * * * | 0 2 :oo:4:xo: .. .. &#xt ♦ 4 2 | 4 4 0 4 | 0 4 0 0 4 0 | * 3N * * * * | 2 0 .. xo 3 ox .. &#x ♦ 3 3 | 3 6 3 0 | 1 3 3 1 0 0 | * * 8N * * * | 1 1 .o 4 .o 3 .x .. ♦ 0 6 | 0 0 12 0 | 0 0 0 8 0 0 | * * * N * * | 2 0 .. :xo:3:ox: .. &#x ♦ 3 3 | 3 0 3 6 | 1 0 0 1 3 3 | * * * * 8N * | 1 1 .. .. :ox:4:oo:&#xt ♦ 2 4 | 0 4 4 4 | 0 0 4 0 0 4 | * * * * * 3N | 0 2 ------------------------+-------+-----------------+-----------------------+-----------------+---- :oo:4:xo:3:ox: .. &#xt ♦ 12 12 | 24 24 24 24 | 8 24 12 16 24 12 | 0 6 8 2 8 0 | N * .. :xo:3:ox:4:oo:&#xt ♦ 12 12 | 24 24 24 24 | 16 12 24 8 12 24 | 2 0 8 0 8 6 | * N
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