2ico+48{4}+128{3}

Acronym	...
Name	2ico+48{4}+128{3} (?)
Circumradius	1
Coordinates	(1, 0, 0, 0) & all permutations, all changes of sign (vertex inscribed q-hex) (±1/2, ±1/2, ±1/2, ±1/2) & all permutations, even number of minus signs (vertex inscribed q-hex) (±1/2, ±1/2, ±1/2, ±1/2) & all permutations, odd number of minus signs (vertex inscribed q-hex) The hull of any pair of those sets describes a tesseracts.
General of army	ico
Colonel of regiment	ico
Confer	non-Grünbaumian master: ico Grünbaumian relatives: 2ico

This scaliform polychoron (having squippy for cells) looks like a compound of 2 coincident icositetrachora (ico) with 48 additional squares arranged pairwise coincident as diagonals of a hexadecachoral subset of octahedra (oct) and 128 additional triangles arranged pairwise coincident in tetrahedral positions of the remaining octahedra.

Incidence matrix according to Dynkin symbol

β3β3o4o

both( . . . . ) | 48 |   8   8 |  4  4  12  4 |  4 1  5
----------------+----+---------+--------------+--------
sefa( s3s . . ) |  2 | 192   * |  1  0   2  0 |  2 0  1
sefa( . β3o . ) |  2 |   * 192 |  0  1   1  1 |  1 1  1
----------------+----+---------+--------------+--------
both( s3s . . ) ♦  3 |   3   0 | 64  *   *  * |  2 0  0
      . β3o .   ♦  3 |   0   3 |  * 64   *  * |  1 1  0
sefa( β3β3o . ) |  3 |   2   1 |  *  * 192  * |  1 0  1
sefa( . β3o4o ) |  4 |   0   4 |  *  *   * 48 |  0 1  1
----------------+----+---------+--------------+--------
      β3β3o .   ♦ 12 |  24  12 |  8  4  12  0 | 16 *  *
      . β3o4o   ♦  6 |   0  24 |  0  8   0  6 |  * 8  *
sefa( β3β3o4o ) ♦  5 |   4   4 |  0  0   4  1 |  * * 48

starting figure: x3x3o4o

β3β3o *b3o

both( . . .    . ) | 48 |   8  4  4 |  4  2  2  6  6  4 | 2 2 1  5
-------------------+----+-----------+-------------------+---------
sefa( s3s .    . ) |  2 | 192  *  * |  1  0  0  1  1  0 | 1 1 0  1
sefa( . β3o    . ) |  2 |   * 96  * |  0  1  0  1  0  1 | 1 0 1  1
sefa( . β . *b3o ) |  2 |   *  * 96 |  0  0  1  0  1  1 | 0 1 1  1
-------------------+----+-----------+-------------------+---------
both( s3s .    . ) ♦  3 |   3  0  0 | 64  *  *  *  *  * | 1 1 0  0
      . β3o    .   ♦  3 |   0  3  0 |  * 32  *  *  *  * | 1 0 1  0
      . β . *b3o   ♦  3 |   0  0  3 |  *  * 32  *  *  * | 0 1 1  0
sefa( β3β3o    . ) |  3 |   2  1  0 |  *  *  * 96  *  * | 1 0 0  1
sefa( β3β . *b3o ) |  3 |   2  0  1 |  *  *  *  * 96  * | 0 1 0  1
sefa( . β3o *b3o ) |  4 |   0  2  2 |  *  *  *  *  * 48 | 0 0 1  1
-------------------+----+-----------+-------------------+---------
      β3β3o    .   ♦ 12 |  24 12  0 |  8  4  0 12  0  0 | 8 * *  *
      β3β . *b3o   ♦ 12 |  24  0 12 |  8  0  4  0 12  0 | * 8 *  *
      . β3o *b3o   ♦  6 |   0 12 12 |  0  4  4  0  0  6 | * * 8  *
sefa( β3β3o *b3o ) ♦  5 |   4  2  2 |  0  0  0  2  2  1 | * * * 48

starting figure: x3x3o *b3o

top of page