Acronym ...
Name gico+8co+16 2thah (?)
Circumradius 1
Confer gico  

This Grünbaumian polychoron is special in that it does not bend to any description as being kind of a blend of simpler single-covered polychora. It is inscribed into the icositetrachoron (ico). It thereby is kind of related to the octihexadecahemihexadecachoron (ohuhoh), at least to the subset of tetrahemihexahedra (thah) contained in that. Those 16 thahs do adjoin all their triangles to one another. But those here are replaced by their double covers, x3o3/2x. So only half of the triangles will be adjoined any longer. Additionally it uses the 4 diametral cuboctahedra (co) of ico. These are to be taken as 2 coincident copies each, thus they match up the remaining triangles. The squares of those 16 2thahs together with those of the co-pairs would be twice of those of the 3 tesseract compound (called "gico", great icositetrachoron), inscribed into ico. So, by adjoining each 2thah-square or co-square to a cube-square makes the cubes to 4-prisms from now on (from extorial symmetry), and the cubes of that compound (infinitesimal taken apart) are matched up by those. So that figure indeed closes dyadicaly.

The vertex figure is contained within that of ico, i.e. within a cube: it uses a diametral rectangle (verf of co), 2 adjacent square(2)-scaled regular triangles (verf of cube) plus 2 crossed squares (verf of thah). But clearly there are 4 vertices of that figure each coincident (coincident to those of the encasing ico). Thus too, 4 such described vertex figures fall together tetragonaly symmetric within the encasing cube.


Incidence matrix according to Dynkin symbol

x3o3x *b3/2x

. . .      . | 96 |  2  2  2 |  1  2  2  1  1  2 | 1 1  1 1
-------------+----+----------+-------------------+---------
x . .      . |  2 | 96  *  * |  1  1  1  0  0  0 | 1 1  1 0
. . x      . |  2 |  * 96  * |  0  1  0  1  0  1 | 1 0  1 1
. . .      x |  2 |  *  * 96 |  0  0  1  0  1  1 | 0 1  1 1
-------------+----+----------+-------------------+---------
x3o .      . |  3 |  3  0  0 | 32  *  *  *  *  * | 1 1  0 0
x . x      . |  4 |  2  2  0 |  * 48  *  *  *  * | 1 0  1 0
x . .      x |  4 |  2  0  2 |  *  * 48  *  *  * | 0 1  1 0
. o3x      . |  3 |  0  3  0 |  *  *  * 32  *  * | 1 0  0 1
. o . *b3/2x |  3 |  0  0  3 |  *  *  *  * 32  * | 0 1  0 1
. . x      x |  4 |  0  2  2 |  *  *  *  *  * 48 | 0 0  1 1
-------------+----+----------+-------------------+---------
x3o3x      .  12 | 12 12  0 |  4  6  0  4  0  0 | 8 *  * *
x3o . *b3/2x  12 | 12  0 12 |  4  0  6  0  4  0 | * 8  * *
x . x      x   8 |  4  4  4 |  0  2  2  0  0  2 | * * 24 *
. o3x *b3/2x  12 |  0 12 12 |  0  0  0  4  4  6 | * *  * 8
or
. . .      .    | 96 |   4  2 |  2  2  4  1 | 1  2  2
----------------+----+--------+-------------+--------
x . .      .  & |  2 | 192  * |  1  1  1  0 | 1  1  1
. . .      x    |  2 |   * 96 |  0  0  2  1 | 0  2  1
----------------+----+--------+-------------+--------
x3o .      .  & |  3 |   3  0 | 64  *  *  * | 1  1  0
x . x      .    |  4 |   4  0 |  * 48  *  * | 1  0  1
x . .      x  & |  4 |   2  2 |  *  * 96  * | 0  1  1
. o . *b3/2x    |  3 |   0  3 |  *  *  * 32 | 0  2  0
----------------+----+--------+-------------+--------
x3o3x      .     12 |  24  0 |  8  6  0  0 | 8  *  *
x3o . *b3/2x  &  12 |  12 12 |  4  0  6  4 | * 16  *
x . x      x      8 |   8  4 |  0  2  4  0 | *  * 24

x3/2o3/2x *b3x

.   .   .    . | 96 |  2  2  2 |  1  2  2  1  1  2 | 1 1  1 1
---------------+----+----------+-------------------+---------
x   .   .    . |  2 | 96  *  * |  1  1  1  0  0  0 | 1 1  1 0
.   .   x    . |  2 |  * 96  * |  0  1  0  1  0  1 | 1 0  1 1
.   .   .    x |  2 |  *  * 96 |  0  0  1  0  1  1 | 0 1  1 1
---------------+----+----------+-------------------+---------
x3/2o   .    . |  3 |  3  0  0 | 32  *  *  *  *  * | 1 1  0 0
x   .   x    . |  4 |  2  2  0 |  * 48  *  *  *  * | 1 0  1 0
x   .   .    x |  4 |  2  0  2 |  *  * 48  *  *  * | 0 1  1 0
.   o3/2x    . |  3 |  0  3  0 |  *  *  * 32  *  * | 1 0  0 1
.   o   . *b3x |  3 |  0  0  3 |  *  *  *  * 32  * | 0 1  0 1
.   .   x    x |  4 |  0  2  2 |  *  *  *  *  * 48 | 0 0  1 1
---------------+----+----------+-------------------+---------
x3/2o3/2x    .  12 | 12 12  0 |  4  6  0  4  0  0 | 8 *  * *
x3/2o   . *b3x  12 | 12  0 12 |  4  0  6  0  4  0 | * 8  * *
x   .   x    x   8 |  4  4  4 |  0  2  2  0  0  2 | * * 24 *
.   o3/2x *b3x  12 |  0 12 12 |  0  0  0  4  4  6 | * *  * 8
or
.   .   .    .    | 96 |   4  2 |  2  2  4  1 | 1  2  2
------------------+----+--------+-------------+--------
x   .   .    .  & |  2 | 192  * |  1  1  1  0 | 1  1  1
.   .   .    x    |  2 |   * 96 |  0  0  2  1 | 0  2  1
------------------+----+--------+-------------+--------
x3/2o   .    .  & |  3 |   3  0 | 64  *  *  * | 1  1  0
x   .   x    .    |  4 |   4  0 |  * 48  *  * | 1  0  1
x   .   .    x  & |  4 |   2  2 |  *  * 96  * | 0  1  1
.   o   . *b3x    |  3 |   0  3 |  *  *  * 32 | 0  2  0
------------------+----+--------+-------------+--------
x3/2o3/2x    .     12 |  24  0 |  8  6  0  0 | 8  *  *
x3/2o   . *b3x  &  12 |  12 12 |  4  0  6  4 | * 16  *
x   .   x    x      8 |   8  4 |  0  2  4  0 | *  * 24

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