Acronym grittip
Name truncated-tesseract prism,
central segment of prin
Circumradius sqrt[23+10 sqrt(2)]/2 = 3.047217
Coordinates ((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations in all but last coord., all changes of sign
Confer
uniform relative:
prin  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x o3x3x4x

. . . . . | 384 |   1   2   1   1 |   2  1  1   1   2   2  1 |  1  2  2  1  1  1  2 |  1  1 2 1
----------+-----+-----------------+--------------------------+----------------------+----------
x . . . . |   2 | 192   *   *   * |   2  1  1   0   0   0  0 |  1  2  2  1  0  0  0 |  1  1 2 0
. . x . . |   2 |   * 384   *   * |   1  0  0   1   1   1  0 |  1  1  1  0  1  1  1 |  1  1 1 1
. . . x . |   2 |   *   * 192   * |   0  1  0   0   2   0  1 |  0  2  0  1  1  0  2 |  1  0 2 1
. . . . x |   2 |   *   *   * 192 |   0  0  1   0   0   2  1 |  0  0  2  1  0  1  2 |  0  1 2 1
----------+-----+-----------------+--------------------------+----------------------+----------
x . x . . |   4 |   2   2   0   0 | 192  *  *   *   *   *  * |  1  1  1  0  0  0  0 |  1  1 1 0
x . . x . |   4 |   2   0   2   0 |   * 96  *   *   *   *  * |  0  2  0  1  0  0  0 |  1  0 2 0
x . . . x |   4 |   2   0   0   2 |   *  * 96   *   *   *  * |  0  0  2  1  0  0  0 |  0  1 2 0
. o3x . . |   3 |   0   3   0   0 |   *  *  * 128   *   *  * |  1  0  0  0  1  1  0 |  1  1 0 1
. . x3x . |   6 |   0   3   3   0 |   *  *  *   * 128   *  * |  0  1  0  0  1  0  1 |  1  0 1 1
. . x . x |   4 |   0   2   0   2 |   *  *  *   *   * 192  * |  0  0  1  0  0  1  1 |  0  1 1 1
. . . x4x |   8 |   0   0   4   4 |   *  *  *   *   *   * 48 |  0  0  0  1  0  0  2 |  0  0 2 1
----------+-----+-----------------+--------------------------+----------------------+----------
x o3x . .    6 |   3   6   0   0 |   3  0  0   2   0   0  0 | 64  *  *  *  *  *  * |  1  1 0 0
x . x3x .   12 |   6   6   6   0 |   3  3  0   0   2   0  0 |  * 64  *  *  *  *  * |  1  0 1 0
x . x . x    8 |   4   4   0   4 |   2  0  2   0   0   2  0 |  *  * 96  *  *  *  * |  0  1 1 0
x . . x4x   16 |   8   0   8   8 |   0  4  4   0   0   0  2 |  *  *  * 24  *  *  * |  0  0 2 0
. o3x3x .   12 |   0  12   6   0 |   0  0  0   4   4   0  0 |  *  *  *  * 32  *  * |  1  0 0 1
. o3x . x    6 |   0   6   0   3 |   0  0  0   2   0   3  0 |  *  *  *  *  * 64  * |  0  1 0 1
. . x3x4x   48 |   0  24  24  24 |   0  0  0   0   8  12  6 |  *  *  *  *  *  * 16 |  0  0 1 1
----------+-----+-----------------+--------------------------+----------------------+----------
x o3x3x .   24 |  12  24  12   0 |  12  6  0   8   8   0  0 |  4  4  0  0  2  0  0 | 16  * * *
x o3x . x   12 |   6  12   0   6 |   6  0  3   4   0   6  0 |  2  0  3  0  0  2  0 |  * 32 * *
x . x3x4x   96 |  48  48  48  48 |  24 24 24   0  16  24 12 |  0  8 12  6  0  0  2 |  *  * 8 * 
. o3x3x4x  192 |   0 192  96  96 |   0  0  0  64  64  96 24 |  0  0  0  0 16 32  8 |  *  * * 2

oo3xx3xx4xx&#x   → height = 1
(grit || grit)

o.3o.3o.4o.    | 192   * |   2  1  1   1   0  0  0 |  1  2  2  1   2  1  1  0  0  0  0 |  1  1 2  1  2  2  1  0  0 0 | 1  1  1 2 0
.o3.o3.o4.o    |   * 192 |   0  0  0   1   2  1  1 |  0  0  0  0   2  1  1  1  2  2  1 |  0  0 0  1  2  2  1  1  1 2 | 0  1  1 2 1
---------------+---------+-------------------------+-----------------------------------+-----------------------------+------------
.. x. .. ..    |   2   0 | 192  *  *   *   *  *  * |  1  1  1  0   1  0  0  0  0  0  0 |  1  1 1  1  1  1  0  0  0 0 | 1  1  1 1 0
.. .. x. ..    |   2   0 |   * 96  *   *   *  *  * |  0  2  0  1   0  1  0  0  0  0  0 |  1  0 2  2  0  1  0  0  0 0 | 1  1  0 2 0
.. .. .. x.    |   2   0 |   *  * 96   *   *  *  * |  0  0  2  1   0  0  1  0  0  0  0 |  0  1 2  0  0  2  1  0  0 0 | 1  0  1 2 0
oo3oo3oo4oo&#x |   1   1 |   *  *  * 192   *  *  * |  0  0  0  0   2  1  1  0  0  0  0 |  0  0 0  1  2  2  1  0  0 0 | 0  1  1 2 0
.. .x .. ..    |   0   2 |   *  *  *   * 192  *  * |  0  0  0  0   1  0  0  1  1  1  0 |  0  0 0  1  1  1  0  1  1 1 | 0  1  1 1 1
.. .. .x ..    |   0   2 |   *  *  *   *   * 96  * |  0  0  0  0   0  1  0  0  2  0  1 |  0  0 0  2  0  1  0  1  0 2 | 0  1  0 2 1
.. .. .. .x    |   0   2 |   *  *  *   *   *  * 96 |  0  0  0  0   0  0  1  0  0  2  1 |  0  0 0  0  0  2  1  0  1 2 | 0  0  1 2 1
---------------+---------+-------------------------+-----------------------------------+-----------------------------+------------
o.3x. .. ..    |   3   0 |   3  0  0   0   0  0  0 | 64  *  *  *   *  *  *  *  *  *  * |  1  1 0  1  0  0  0  0  0 0 | 1  1  1 0 0
.. x.3x. ..    |   6   0 |   3  3  0   0   0  0  0 |  * 64  *  *   *  *  *  *  *  *  * |  1  0 1  0  1  0  0  0  0 0 | 1  1  0 1 0
.. x. .. x.    |   4   0 |   2  0  2   0   0  0  0 |  *  * 96  *   *  *  *  *  *  *  * |  0  1 1  0  0  1  0  0  0 0 | 1  0  1 1 0
.. .. x.4x.    |   8   0 |   0  4  4   0   0  0  0 |  *  *  * 24   *  *  *  *  *  *  * |  0  0 2  0  0  0  1  0  0 0 | 1  0  0 2 0
.. xx .. ..&#x |   2   2 |   1  0  0   2   1  0  0 |  *  *  *  * 192  *  *  *  *  *  * |  0  0 0  1  1  1  0  0  0 0 | 0  1  1 1 0
.. .. xx ..&#x |   2   2 |   0  1  0   2   0  1  0 |  *  *  *  *   * 96  *  *  *  *  * |  0  0 0  2  0  1  0  0  0 0 | 0  1  0 2 0
.. .. .. xx&#x |   2   2 |   0  0  1   2   0  0  1 |  *  *  *  *   *  * 96  *  *  *  * |  0  0 0  0  0  2  1  0  0 0 | 0  0  1 2 0
.o3.x .. ..    |   0   3 |   0  0  0   0   3  0  0 |  *  *  *  *   *  *  * 64  *  *  * |  0  0 0  1  0  0  0  1  1 0 | 0  1  1 0 1
.. .x3.x ..    |   0   6 |   0  0  0   0   3  3  0 |  *  *  *  *   *  *  *  * 64  *  * |  0  0 0  0  1  0  0  1  0 1 | 0  1  0 1 1
.. .x .. .x    |   0   4 |   0  0  0   0   2  0  2 |  *  *  *  *   *  *  *  *  * 96  * |  0  0 0  0  0  1  0  0  1 1 | 0  0  1 1 1
.. .. .x4.x    |   0   8 |   0  0  0   0   0  4  4 |  *  *  *  *   *  *  *  *  *  * 24 |  0  0 0  0  0  0  1  0  0 2 | 0  0  0 2 1
---------------+---------+-------------------------+-----------------------------------+-----------------------------+------------
o.3x.3x. ..      12   0 |  12  6  0   0   0  0  0 |  4  4  0  0   0  0  0  0  0  0  0 | 16  * *  *  *  *  *  *  * * | 1  1  0 0 0
o.3x. .. x.       6   0 |   6  0  3   0   0  0  0 |  2  0  3  0   0  0  0  0  0  0  0 |  * 32 *  *  *  *  *  *  * * | 1  0  1 0 0
.. x.3x.4x.      48   0 |  24 24 24   0   0  0  0 |  0  8 12  6   0  0  0  0  0  0  0 |  *  * 8  *  *  *  *  *  * * | 1  0  0 1 0
oo3xx .. ..&#x    3   3 |   3  0  0   3   3  0  0 |  1  0  0  0   3  0  0  1  0  0  0 |  *  * * 64  *  *  *  *  * * | 0  1  1 0 0
.. xx3xx ..&#x    6   6 |   3  3  0   6   3  3  0 |  0  1  0  0   3  3  0  0  1  0  0 |  *  * *  * 64  *  *  *  * * | 0  1  0 1 0
.. xx .. xx&#x    4   4 |   2  0  2   4   2  0  2 |  0  0  1  0   2  0  2  0  0  1  0 |  *  * *  *  * 96  *  *  * * | 0  0  1 1 0
.. .. xx4xx&#x    8   8 |   0  4  4   8   0  4  4 |  0  0  0  1   0  4  4  0  0  0  1 |  *  * *  *  *  * 24  *  * * | 0  0  0 2 0
.o3.x3.x ..       0  12 |   0  0  0   0  12  6  0 |  0  0  0  0   0  0  0  4  4  0  0 |  *  * *  *  *  *  * 16  * * | 0  1  0 0 1
.o3.x .. .x       0   6 |   0  0  0   0   6  0  3 |  0  0  0  0   0  0  0  2  0  3  0 |  *  * *  *  *  *  *  * 32 * | 0  0  1 0 1
.. .x3.x4.x       0  48 |   0  0  0   0  24 24 24 |  0  0  0  0   0  0  0  0  8 12  6 |  *  * *  *  *  *  *  *  * 8 | 0  0  0 1 1
---------------+---------+-------------------------+-----------------------------------+-----------------------------+------------
o.3x.3x.4x.     192   0 | 192 96 96   0   0  0  0 | 64 64 96 24   0  0  0  0  0  0  0 | 16 32 8  0  0  0  0  0  0 0 | 1  *  * * *
oo3xx3xx ..&#x   12  12 |  12  6  0  12  12  6  0 |  4  4  0  0  12  6  0  4  4  0  0 |  1  0 0  4  4  0  0  1  0 0 | * 16  * * *
oo3xx .. xx&#x    6   6 |   6  0  3   6   6  0  3 |  2  0  3  0   6  0  3  2  0  3  0 |  0  1 0  2  0  3  0  0  1 0 | *  * 32 * *
.. xx3xx4xx&#x   48  48 |  24 24 24  48  24 24 24 |  0  8 12  6  24 24 24  0  8 12  6 |  0  0 1  0  8 12  6  0  0 1 | *  *  * 8 *
.o3.x3.x4.x       0 192 |   0  0  0   0 192 96 96 |  0  0  0  0   0  0  0 64 64 96 24 |  0  0 0  0  0  0  0 16 32 8 | *  *  * * 1

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