Acronym thexip
Name truncated-hexadecachoron prism
Circumradius sqrt(11)/2 = 1.658312
Coordinates (sqrt(2), 1/sqrt(2), 0, 0)   & all permutations in all but last coord., all changes of sign
Confer
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

x x3x3o4o

. . . . . | 96 |  1  1   4 |  1  4  4   4 |  4  4  4  1 |  4 1 1
----------+----+-----------+--------------+-------------+-------
x . . . . |  2 | 48  *   * |  1  4  0   0 |  4  4  0  0 |  4 1 0
. x . . . |  2 |  * 48   * |  1  0  4   0 |  4  0  4  0 |  4 0 1
. . x . . |  2 |  *  * 192 |  0  1  1   2 |  1  2  2  1 |  2 1 1
----------+----+-----------+--------------+-------------+-------
x x . . . |  4 |  2  2   0 | 24  *  *   * |  4  0  0  0 |  4 0 0
x . x . . |  4 |  2  0   2 |  * 96  *   * |  1  2  0  0 |  2 1 0
. x3x . . |  6 |  0  3   3 |  *  * 64   * |  1  0  2  0 |  2 0 1
. . x3o . |  3 |  0  0   3 |  *  *  * 128 |  0  1  1  1 |  1 1 1
----------+----+-----------+--------------+-------------+-------
x x3x . .  12 |  6  6   6 |  3  3  2   0 | 32  *  *  * |  2 0 0
x . x3o .   6 |  3  0   6 |  0  3  0   2 |  * 64  *  * |  1 1 0
. x3x3o .  12 |  0  6  12 |  0  0  4   4 |  *  * 32  * |  1 0 1
. . x3o4o   6 |  0  0  12 |  0  0  0   8 |  *  *  * 16 |  0 1 1
----------+----+-----------+--------------+-------------+-------
x x3x3o .  24 | 12 12  24 |  6 12  8   8 |  4  4  2  0 | 16 * *
x . x3o4o  12 |  6  0  24 |  0 12  0  16 |  0  8  0  2 |  * 8 *
. x3x3o4o  48 |  0 24  96 |  0  0 32  64 |  0  0 16  8 |  * * 2

x x3x3o *c3o

. . . .    . | 96 |  1  1   4 |  1  4  4  2  2 |  4  2  2  2  2  1 | 2 2 1 1
-------------+----+-----------+----------------+-------------------+--------
x . . .    . |  2 | 48  *   * |  1  4  0  0  0 |  4  2  2  0  0  0 | 2 2 1 0
. x . .    . |  2 |  * 48   * |  1  0  4  0  0 |  4  0  0  2  2  0 | 2 2 0 1
. . x .    . |  2 |  *  * 192 |  0  1  1  1  1 |  1  1  1  1  1  1 | 1 1 1 1
-------------+----+-----------+----------------+-------------------+--------
x x . .    . |  4 |  2  2   0 | 24  *  *  *  * |  4  0  0  0  0  0 | 2 2 0 0
x . x .    . |  4 |  2  0   2 |  * 96  *  *  * |  1  1  1  0  0  0 | 1 1 1 0
. x3x .    . |  6 |  0  3   3 |  *  * 64  *  * |  1  0  0  1  1  0 | 1 1 0 1
. . x3o    . |  3 |  0  0   3 |  *  *  * 64  * |  0  1  0  1  0  1 | 1 0 1 1
. . x . *c3o |  3 |  0  0   3 |  *  *  *  * 64 |  0  0  1  0  1  1 | 0 1 1 1
-------------+----+-----------+----------------+-------------------+--------
x x3x .    .  12 |  6  6   6 |  3  3  2  0  0 | 32  *  *  *  *  * | 1 1 0 0
x . x3o    .   6 |  3  0   6 |  0  3  0  2  0 |  * 32  *  *  *  * | 1 0 1 0
x . x . *c3o   6 |  3  0   6 |  0  3  0  0  2 |  *  * 32  *  *  * | 0 1 1 0
. x3x3o    .  12 |  0  6  12 |  0  0  4  4  0 |  *  *  * 16  *  * | 1 0 0 1
. x3x . *c3o  12 |  0  6  12 |  0  0  4  0  4 |  *  *  *  * 16  * | 0 1 0 1
. . x3o *c3o   6 |  0  0  12 |  0  0  0  4  4 |  *  *  *  *  * 16 | 0 0 1 1
-------------+----+-----------+----------------+-------------------+--------
x x3x3o    .  24 | 12 12  24 |  6 12  8  8  0 |  4  4  0  2  0  0 | 8 * * *
x x3x . *c3o  24 | 12 12  24 |  6 12  8  0  8 |  4  0  4  0  2  0 | * 8 * *
x . x3o *c3o  12 |  6  0  24 |  0 12  0  8  8 |  0  4  4  0  0  2 | * * 8 *
. x3x3o *c3o  48 |  0 24  96 |  0  0 32 32 32 |  0  0  0  8  8  8 | * * * 2

xx3xx3oo4oo&#x   → height = 1
(thex  || thex)

...

xx3xx3oo *b3oo&#x   → height = 1
(thex  || thex)

o.3o.3o. *b3o.    | 48  * |  1  4  1  0  0 |  4  2  2  1  4  0  0  0 | 2 2 1  4  2  2 0 0 0 | 1 2 2 1 0
.o3.o3.o *b3.o    |  * 48 |  0  0  1  1  4 |  0  0  0  1  4  4  2  2 | 0 0 0  4  2  2 2 2 1 | 0 2 2 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x. .. ..    ..    |  2  0 | 24  *  *  *  * |  4  0  0  1  0  0  0  0 | 2 2 0  4  0  0 0 0 0 | 1 2 2 0 0
.. x. ..    ..    |  2  0 |  * 96  *  *  * |  1  1  1  0  1  0  0  0 | 1 1 1  1  1  1 0 0 0 | 1 1 1 1 0
oo3oo3oo *b3oo&#x |  1  1 |  *  * 48  *  * |  0  0  0  1  4  0  0  0 | 0 0 0  4  2  2 0 0 0 | 0 2 2 1 0
.x .. ..    ..    |  0  2 |  *  *  * 24  * |  0  0  0  1  0  4  0  0 | 0 0 0  4  0  0 2 2 0 | 0 2 2 0 1
.. .x ..    ..    |  0  2 |  *  *  *  * 96 |  0  0  0  0  1  1  1  1 | 0 0 0  1  1  1 1 1 1 | 0 1 1 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x.3x. ..    ..    |  6  0 |  3  3  0  0  0 | 32  *  *  *  *  *  *  * | 1 1 0  1  0  0 0 0 0 | 1 1 1 0 0
.. x.3o.    ..    |  3  0 |  0  3  0  0  0 |  * 32  *  *  *  *  *  * | 1 0 1  0  1  0 0 0 0 | 1 1 0 1 0
.. x. .. *b3o.    |  3  0 |  0  3  0  0  0 |  *  * 32  *  *  *  *  * | 0 1 1  0  0  1 0 0 0 | 1 0 1 1 0
xx .. ..    ..&#x |  2  2 |  1  0  2  1  0 |  *  *  * 24  *  *  *  * | 0 0 0  4  0  0 0 0 0 | 0 2 2 0 0
.. xx ..    ..&#x |  2  2 |  0  1  2  0  1 |  *  *  *  * 96  *  *  * | 0 0 0  1  1  1 0 0 0 | 0 1 1 1 0
.x3.x ..    ..    |  0  6 |  0  0  0  3  3 |  *  *  *  *  * 32  *  * | 0 0 0  1  0  0 1 1 0 | 0 1 1 0 1
.. .x3.o    ..    |  0  3 |  0  0  0  0  3 |  *  *  *  *  *  * 32  * | 0 0 0  0  1  0 1 0 1 | 0 1 0 1 1
.. .x .. *b3.o    |  0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  * 32 | 0 0 0  0  0  1 0 1 1 | 0 0 1 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x.3x.3o.    ..     12  0 |  6 12  0  0  0 |  4  4  0  0  0  0  0  0 | 8 * *  *  *  * * * * | 1 1 0 0 0
x.3x. .. *b3o.     12  0 |  6 12  0  0  0 |  4  0  4  0  0  0  0  0 | * 8 *  *  *  * * * * | 1 0 1 0 0
.. x.3o. *b3o.      6  0 |  0 12  0  0  0 |  0  4  4  0  0  0  0  0 | * * 8  *  *  * * * * | 1 0 0 1 0
xx3xx ..    ..&#x   6  6 |  3  3  6  3  3 |  1  0  0  3  3  1  0  0 | * * * 32  *  * * * * | 0 1 1 0 0
.. xx3oo    ..&#x   3  3 |  0  3  3  0  3 |  0  1  0  0  3  0  1  0 | * * *  * 32  * * * * | 0 1 0 1 0
.. xx .. *b3oo&#x   3  3 |  0  3  3  0  3 |  0  0  1  0  3  0  0  1 | * * *  *  * 32 * * * | 0 0 1 1 0
.x3.x3.o    ..      0 12 |  0  0  0  6 12 |  0  0  0  0  0  4  4  0 | * * *  *  *  * 8 * * | 0 1 0 0 1
.x3.x .. *b3.o      0 12 |  0  0  0  6 12 |  0  0  0  0  0  4  0  4 | * * *  *  *  * * 8 * | 0 0 1 0 1
.. .x3.o *b3.o      0  6 |  0  0  0  0 12 |  0  0  0  0  0  0  4  4 | * * *  *  *  * * * 8 | 0 0 0 1 1
------------------+-------+----------------+-------------------------+----------------------+----------
x.3x.3o. *b3o.     48  0 | 24 96  0  0  0 | 32 32 32  0  0  0  0  0 | 8 8 8  0  0  0 0 0 0 | 1 * * * *
xx3xx3oo    ..&#x  12 12 |  6 12 12  6 12 |  4  4  0  6 12  4  4  0 | 1 0 0  4  4  0 1 0 0 | * 8 * * *
xx3xx .. *b3oo&#x  12 12 |  6 12 12  6 12 |  4  0  4  6 12  4  0  4 | 0 1 0  4  0  4 0 1 0 | * * 8 * *
.. xx3oo *b3oo&#x   6  6 |  0 12  6  0 12 |  0  4  4  0 12  0  4  4 | 0 0 1  0  4  4 0 0 1 | * * * 8 *
.x3.x3.o *b3.o      0 48 |  0  0  0 24 96 |  0  0  0  0  0 32 32 32 | 0 0 0  0  0  0 8 8 8 | * * * * 1

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