Acronym icot
Name icositetrachoric tetracomb,
Voronoi complex of body-centered tesseractic (bct) lattice
Coordinates
  1. (i, j, k, l)                                    i.e. all integer touples (inscribed test) and
  2. (i+1/2, j+1/2, k+1/2, l+1/2)     i.e. half-integer touples with i+j+k+l even (body centers of alternate tes only)
Dual hext
Confer
related tesselations:
Delone complex of primitive tesseractic lattice   Voronoi complex of primitive tesseractic lattice   Delone complex of bct lattice  
general polytopal classes:
partial Stott expansions  
External
links
wikipedia

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

© 2004-2018
top of page