Acronym tahp Name tesseractihexadecachoron prism,bitruncated-tesseract prism,bitruncated-hexadecachoron prism Circumradius sqrt(19)/2 = 2.179449 Coordinates (sqrt(2), sqrt(2), 1/sqrt(2), 0, 1/2)   & all permutations in all but last coord., all changes of sign Confer general polytopal classes: segmentotera

Incidence matrix according to Dynkin symbol

```x o3x3x4o

. . . . . | 192 |  1   2   2 |  2  2  1   4  1 |  1  4  1  2  2 |  2 2 1
----------+-----+------------+-----------------+----------------+-------
x . . . . |   2 | 96   *   * |  2  2  0   0  0 |  1  4  1  0  0 |  2 2 0
. . x . . |   2 |  * 192   * |  1  0  1   2  0 |  1  2  0  2  1 |  2 1 1
. . . x . |   2 |  *   * 192 |  0  1  0   2  1 |  0  2  1  1  2 |  1 2 1
----------+-----+------------+-----------------+----------------+-------
x . x . . |   4 |  2   2   0 | 96  *  *   *  * |  1  2  0  0  0 |  2 1 0
x . . x . |   4 |  2   0   2 |  * 96  *   *  * |  0  2  1  0  0 |  1 2 0
. o3x . . |   3 |  0   3   0 |  *  * 64   *  * |  1  0  0  2  0 |  2 0 1
. . x3x . |   6 |  0   3   3 |  *  *  * 128  * |  0  1  0  1  1 |  1 1 1
. . . x4o |   4 |  0   0   4 |  *  *  *   * 48 |  0  0  1  0  2 |  0 2 1
----------+-----+------------+-----------------+----------------+-------
x o3x . . ♦   6 |  3   6   0 |  3  0  2   0  0 | 32  *  *  *  * |  2 0 0
x . x3x . ♦  12 |  6   6   6 |  3  3  0   2  0 |  * 64  *  *  * |  1 1 0
x . . x4o ♦   8 |  4   0   8 |  0  4  0   0  2 |  *  * 24  *  * |  0 2 0
. o3x3x . ♦  12 |  0  12   6 |  0  0  4   4  0 |  *  *  * 32  * |  1 0 1
. . x3x4o ♦  24 |  0  12  24 |  0  0  0   8  6 |  *  *  *  * 16 |  0 1 1
----------+-----+------------+-----------------+----------------+-------
x o3x3x . ♦  24 | 12  24  12 | 12  6  8   8  0 |  4  4  0  2  0 | 16 * *
x . x3x4o ♦  48 | 24  24  48 | 12 24  0  16 12 |  0  8  6  0  2 |  * 8 *
. o3x3x4o ♦  96 |  0  96  96 |  0  0 32  64 24 |  0  0  0 16  8 |  * * 2
```

```x x3x3x *c3o

. . . .    . | 192 |  1  1   2  1 |  1  2  1  2  1  2  1 |  2  1  2  1  2  1  1 | 2 1 1 1
-------------+-----+--------------+----------------------+----------------------+--------
x . . .    . |   2 | 96  *   *  * |  1  2  1  0  0  0  0 |  2  1  2  1  0  0  0 | 2 1 1 0
. x . .    . |   2 |  * 96   *  * |  1  0  0  2  1  0  0 |  2  1  0  0  2  1  0 | 2 1 0 1
. . x .    . |   2 |  *  * 192  * |  0  1  0  1  0  1  1 |  1  0  1  1  1  1  1 | 1 1 1 1
. . . x    . |   2 |  *  *   * 96 |  0  0  1  0  1  2  0 |  0  1  2  0  2  0  1 | 2 0 1 1
-------------+-----+--------------+----------------------+----------------------+--------
x x . .    . |   4 |  2  2   0  0 | 48  *  *  *  *  *  * |  2  1  0  0  0  0  0 | 2 1 0 0
x . x .    . |   4 |  2  0   2  0 |  * 96  *  *  *  *  * |  1  0  1  1  0  0  0 | 1 1 1 0
x . . x    . |   4 |  2  0   0  2 |  *  * 48  *  *  *  * |  0  1  2  0  0  0  0 | 2 0 1 0
. x3x .    . |   6 |  0  3   3  0 |  *  *  * 64  *  *  * |  1  0  0  0  1  1  0 | 1 1 0 1
. x . x    . |   4 |  0  2   0  2 |  *  *  *  * 48  *  * |  0  1  0  0  2  0  0 | 2 0 0 1
. . x3x    . |   6 |  0  0   3  3 |  *  *  *  *  * 64  * |  0  0  1  0  1  0  1 | 1 0 1 1
. . x . *c3o |   3 |  0  0   3  0 |  *  *  *  *  *  * 64 |  0  0  0  1  0  1  1 | 0 1 1 1
-------------+-----+--------------+----------------------+----------------------+--------
x x3x .    . ♦  12 |  6  6   6  0 |  3  3  0  2  0  0  0 | 32  *  *  *  *  *  * | 1 1 0 0
x x . x    . ♦   8 |  4  4   0  4 |  2  0  2  0  2  0  0 |  * 24  *  *  *  *  * | 2 0 0 0
x . x3x    . ♦  12 |  6  0   6  6 |  0  3  3  0  0  2  0 |  *  * 32  *  *  *  * | 1 0 1 0
x . x . *c3o ♦   6 |  3  0   6  0 |  0  3  0  0  0  0  2 |  *  *  * 32  *  *  * | 0 1 1 0
. x3x3x    . ♦  24 |  0 12  12 12 |  0  0  0  4  6  4  0 |  *  *  *  * 16  *  * | 1 0 0 1
. x3x . *c3o ♦  12 |  0  6  12  0 |  0  0  0  4  0  0  4 |  *  *  *  *  * 16  * | 0 1 0 1
. . x3x *c3o ♦  12 |  0  0  12  6 |  0  0  0  0  0  4  4 |  *  *  *  *  *  * 16 | 0 0 1 1
-------------+-----+--------------+----------------------+----------------------+--------
x x3x3x    . ♦  48 | 24 24  24 24 | 12 12 12  8 12  8  0 |  4  6  4  0  2  0  0 | 8 * * *
x x3x . *c3o ♦  24 | 12 12  24  0 |  6 12  0  8  0  0  8 |  4  0  0  4  0  2  0 | * 8 * *
x . x3x *c3o ♦  24 | 12  0  24 12 |  0 12  6  0  0  8  8 |  0  0  4  4  0  0  2 | * * 8 *
. x3x3x *c3o ♦  96 |  0 48  96 48 |  0  0  0 32 24 32 32 |  0  0  0  0  8  8  8 | * * * 2
```

```oo3xx3xx4oo&#x   → height = 1
(tah || tah)

...
```

```xx3xx3xx *b3oo&#x   → height = 1
(tah || tah)

o.3o.3o. *b3o.    | 96  * |  1  2  1  1  0  0  0 |  2  1  2  1  1  2  1  0  0  0  0 | 2 1 1  2  1  2  1 0 0 0 | 1 2 1 1 0
.o3.o3.o *b3.o    |  * 96 |  0  0  0  1  1  2  1 |  0  0  0  0  1  2  1  2  1  2  1 | 0 0 0  2  1  2  1 2 1 1 | 0 2 1 1 1
------------------+-------+----------------------+----------------------------------+-------------------------+----------
x. .. ..    ..    |  2  0 | 48  *  *  *  *  *  * |  2  1  0  0  1  0  0  0  0  0  0 | 2 1 0  2  1  0  0 0 0 0 | 1 2 1 0 0
.. x. ..    ..    |  2  0 |  * 96  *  *  *  *  * |  1  0  1  1  0  1  0  0  0  0  0 | 1 1 1  1  0  1  1 0 0 0 | 1 1 1 1 0
.. .. x.    ..    |  2  0 |  *  * 48  *  *  *  * |  0  1  2  0  0  0  1  0  0  0  0 | 2 0 1  0  1  2  0 0 0 0 | 1 2 0 1 0
oo3oo3oo *b3oo&#x |  1  1 |  *  *  * 96  *  *  * |  0  0  0  0  1  2  1  0  0  0  0 | 0 0 0  2  1  2  1 0 0 0 | 0 2 1 1 0
.x .. ..    ..    |  0  2 |  *  *  *  * 48  *  * |  0  0  0  0  1  0  0  2  1  0  0 | 0 0 0  2  1  0  0 2 1 0 | 0 2 1 0 1
.. .x ..    ..    |  0  2 |  *  *  *  *  * 96  * |  0  0  0  0  0  1  0  1  0  1  1 | 0 0 0  1  0  1  1 1 1 1 | 0 1 1 1 1
.. .. .x    ..    |  0  2 |  *  *  *  *  *  * 48 |  0  0  0  0  0  0  1  0  1  2  0 | 0 0 0  0  1  2  0 2 0 1 | 0 2 0 1 1
------------------+-------+----------------------+----------------------------------+-------------------------+----------
x.3x. ..    ..    |  6  0 |  3  3  0  0  0  0  0 | 32  *  *  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  0 0 0 0 | 1 1 1 0 0
x. .. x.    ..    |  4  0 |  2  0  2  0  0  0  0 |  * 24  *  *  *  *  *  *  *  *  * | 2 0 0  0  1  0  0 0 0 0 | 1 2 0 0 0
.. x.3x.    ..    |  6  0 |  0  3  3  0  0  0  0 |  *  * 32  *  *  *  *  *  *  *  * | 1 0 1  0  0  1  0 0 0 0 | 1 1 0 1 0
.. x. .. *b3o.    |  3  0 |  0  3  0  0  0  0  0 |  *  *  * 32  *  *  *  *  *  *  * | 0 1 1  0  0  0  1 0 0 0 | 1 0 1 1 0
xx .. ..    ..&#x |  2  2 |  1  0  0  2  1  0  0 |  *  *  *  * 48  *  *  *  *  *  * | 0 0 0  2  1  0  0 0 0 0 | 0 2 1 0 0
.. xx ..    ..&#x |  2  2 |  0  1  0  2  0  1  0 |  *  *  *  *  * 96  *  *  *  *  * | 0 0 0  1  0  1  1 0 0 0 | 0 1 1 1 0
.. .. xx    ..&#x |  2  2 |  0  0  1  2  0  0  1 |  *  *  *  *  *  * 48  *  *  *  * | 0 0 0  0  1  2  0 0 0 0 | 0 2 0 1 0
.x3.x ..    ..    |  0  6 |  0  0  0  0  3  3  0 |  *  *  *  *  *  *  * 32  *  *  * | 0 0 0  1  0  0  0 1 1 0 | 0 1 1 0 1
.x .. .x    ..    |  0  4 |  0  0  0  0  2  0  2 |  *  *  *  *  *  *  *  * 24  *  * | 0 0 0  0  1  0  0 2 0 0 | 0 2 0 0 1
.. .x3.x    ..    |  0  6 |  0  0  0  0  0  3  3 |  *  *  *  *  *  *  *  *  * 32  * | 0 0 0  0  0  1  0 1 0 1 | 0 1 0 1 1
.. .x .. *b3.o    |  0  3 |  0  0  0  0  0  3  0 |  *  *  *  *  *  *  *  *  *  * 32 | 0 0 0  0  0  0  1 0 1 1 | 0 0 1 1 1
------------------+-------+----------------------+----------------------------------+-------------------------+----------
x.3x.3x.    ..    ♦ 24  0 | 12 12 12  0  0  0  0 |  4  6  4  0  0  0  0  0  0  0  0 | 8 * *  *  *  *  * * * * | 1 1 0 0 0
x.3x. .. *b3o.    ♦ 12  0 |  6 12  0  0  0  0  0 |  4  0  0  4  0  0  0  0  0  0  0 | * 8 *  *  *  *  * * * * | 1 0 1 0 0
.. x.3x. *b3o.    ♦ 12  0 |  0 12  6  0  0  0  0 |  0  0  4  4  0  0  0  0  0  0  0 | * * 8  *  *  *  * * * * | 1 0 0 1 0
xx3xx ..    ..&#x ♦  6  6 |  3  3  0  6  3  3  0 |  1  0  0  0  3  3  0  1  0  0  0 | * * * 32  *  *  * * * * | 0 1 1 0 0
xx .. xx    ..&#x ♦  4  4 |  2  0  2  4  2  0  2 |  0  1  0  0  2  0  2  0  1  0  0 | * * *  * 24  *  * * * * | 0 2 0 0 0
.. xx3xx    ..&#x ♦  6  6 |  0  3  3  6  0  3  3 |  0  0  1  0  0  3  3  0  0  1  0 | * * *  *  * 32  * * * * | 0 1 0 1 0
.. xx .. *b3oo&#x ♦  3  3 |  0  3  0  3  0  3  0 |  0  0  0  1  0  3  0  0  0  0  1 | * * *  *  *  * 32 * * * | 0 0 1 1 0
.x3.x3.x    ..    ♦  0 24 |  0  0  0  0 12 12 12 |  0  0  0  0  0  0  0  4  6  4  0 | * * *  *  *  *  * 8 * * | 0 1 0 0 1
.x3.x .. *b3.o    ♦  0 12 |  0  0  0  0  6 12  0 |  0  0  0  0  0  0  0  4  0  0  4 | * * *  *  *  *  * * 8 * | 0 0 1 0 1
.. .x3.x *b3.o    ♦  0 12 |  0  0  0  0  0 12  6 |  0  0  0  0  0  0  0  0  0  4  4 | * * *  *  *  *  * * * 8 | 0 0 0 1 1
------------------+-------+----------------------+----------------------------------+-------------------------+----------
x.3x.3x. *b3o.    ♦ 96  0 | 48 96 48  0  0  0  0 | 32 24 32 32  0  0  0  0  0  0  0 | 8 8 8  0  0  0  0 0 0 0 | 1 * * * *
xx3xx3xx    ..&#x ♦ 24 24 | 12 12 12 24 12 12 12 |  4  6  4  0 12 12 12  4  6  4  0 | 1 0 0  4  6  4  0 1 0 0 | * 8 * * *
xx3xx .. *b3oo&#x ♦ 12 12 |  6 12  0 12  6 12  0 |  4  0  0  4  6 12  0  4  0  0  4 | 0 1 0  4  0  0  4 0 1 0 | * * 8 * *
.. xx3xx *b3oo&#x ♦ 12 12 |  0 12  6 12  0 12  6 |  0  0  4  4  0 12  6  0  0  4  4 | 0 0 1  0  0  4  4 0 0 1 | * * * 8 *
.x3.x3.x *b3.o    ♦  0 96 |  0  0  0  0 48 96 48 |  0  0  0  0  0  0  0 32 24 32 32 | 0 0 0  0  0  0  0 8 8 8 | * * * * 1
```