Acronym icope
Name icositetrachoron prism
Circumradius sqrt(5)/2 = 1.118034
Coordinates
    1. (1, 0, 0, 0, 1/2)                & all permutations in all but last coord., all changes of sign
    2. (1/2, 1/2, 1/2, 1/2, 1/2)   & all permutations in all but last coord., all changes of sign
  • or just   (1/sqrt(2), 1/sqrt(2), 0, 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 x3o4o3o

. . . . . | 48 |  1   8 |  8  12 | 12  6 |  6 1
----------+----+--------+--------+-------+-----
x . . . . |  2 | 24   *   8   0 | 12  0 |  6 0
. x . . . |  2 |  * 192 |  1   3 |  3  3 |  3 1
----------+----+--------+--------+-------+-----
x x . . . |  4 |  2   2 | 96   * |  3  0 |  3 0
. x3o . . |  3 |  0   3 |  * 192 |  1  2 |  2 1
----------+----+--------+--------+-------+-----
x x3o . .   6 |  3   6 |  3   2 | 96  * |  2 0
. x3o4o .   6 |  0  12 |  0   8 |  * 48 |  1 1
----------+----+--------+--------+-------+-----
x x3o4o .  12 |  6  24 | 12  16 |  8  2 | 24 *
. x3o4o3o  24 |  0  96 |  0  96 |  0 24 |  * 2

x o3x3o4o

. . . . . | 48 |  1   8 |  8  4   8 |  4  8  4  2 |  4 2 1
----------+----+--------+-----------+-------------+-------
x . . . . |  2 | 24   *   8  0   0 |  4  8  0  0 |  4 2 0
. . x . . |  2 |  * 192 |  1  1   2 |  1  2  2  1 |  2 1 1
----------+----+--------+-----------+-------------+-------
x . x . . |  4 |  2   2 | 96  *   * |  1  2  0  0 |  2 1 0
. o3x . . |  3 |  0   3 |  * 64   * |  1  0  2  0 |  2 0 1
. . x3o . |  3 |  0   3 |  *  * 128 |  0  1  1  1 |  1 1 1
----------+----+--------+-----------+-------------+-------
x o3x . .   6 |  3   6 |  3  2   0 | 32  *  *  * |  2 0 0
x . x3o .   6 |  3   6 |  3  0   2 |  * 64  *  * |  1 1 0
. o3x3o .   6 |  0  12 |  0  4   4 |  *  * 32  * |  1 0 1
. . x3o4o   6 |  0  12 |  0  0   8 |  *  *  * 16 |  0 1 1
----------+----+--------+-----------+-------------+-------
x o3x3o .  12 |  6  24 | 12  8   8 |  4  4  2  0 | 16 * *
x . x3o4o  12 |  6  24 | 12  0  16 |  0  8  0  2 |  * 8 *
. o3x3o4o  24 |  0  96 |  0 32  64 |  0  0 16  8 |  * * 2

x o3x3o *c3o

. . . .    . | 48 |  1   8 |  8  4  4  4 |  4  4  4  2  2  2 | 2 2 2 1
-------------+----+--------+-------------+-------------------+--------
x . . .    . |  2 | 24   *   8  0  0  0 |  4  4  4  0  0  0 | 2 2 2 0
. . x .    . |  2 |  * 192 |  1  1  1  1 |  1  1  1  1  1  1 | 1 1 1 1
-------------+----+--------+-------------+-------------------+--------
x . x .    . |  4 |  2   2 | 96  *  *  * |  1  1  1  0  0  0 | 1 1 1 0
. o3x .    . |  3 |  0   3 |  * 64  *  * |  1  0  0  1  1  0 | 1 1 0 1
. . x3o    . |  3 |  0   3 |  *  * 64  * |  0  1  0  1  0  1 | 1 0 1 1
. . x . *c3o |  3 |  0   3 |  *  *  * 64 |  0  0  1  0  1  1 | 0 1 1 1
-------------+----+--------+-------------+-------------------+--------
x o3x .    .   6 |  3   6 |  3  2  0  0 | 32  *  *  *  *  * | 1 1 0 0
x . x3o    .   6 |  3   6 |  3  0  2  0 |  * 32  *  *  *  * | 1 0 1 0
x . x . *c3o   6 |  3   6 |  3  0  0  2 |  *  * 32  *  *  * | 0 1 1 0
. o3x3o    .   6 |  0  12 |  0  4  4  0 |  *  *  * 16  *  * | 1 0 0 1
. o3x . *c3o   6 |  0  12 |  0  4  0  4 |  *  *  *  * 16  * | 0 1 0 1
. . x3o *c3o   6 |  0  12 |  0  0  4  4 |  *  *  *  *  * 16 | 0 0 1 1
-------------+----+--------+-------------+-------------------+--------
x o3x3o    .  12 |  6  24 | 12  8  8  0 |  4  4  0  2  0  0 | 8 * * *
x o3x . *c3o  12 |  6  24 | 12  8  0  8 |  4  0  4  0  2  0 | * 8 * *
x . x3o *c3o  12 |  6  24 | 12  0  8  8 |  0  4  4  0  0  2 | * * 8 *
. o3x3o *c3o  24 |  0  96 |  0 32 32 32 |  0  0  0  8  8  8 | * * * 2

xx3oo4oo3oo&#x   → height = 1
(ico || ico)

...

oo3xx3oo4oo&#x   → height = 1
(ico || ico)

...

oo3xx3oo *b3oo&#x   → height = 1
(ico || ico)

o.3o.3o. *b3o.    | 24  * |  8  1  0 |  4  4  4  8  0  0  0 | 2 2 2  4  4  4 0 0 0 | 1 2 2 2 0
.o3.o3.o *b3.o    |  * 24 |  0  1  8 |  0  0  0  8  4  4  4 | 0 0 0  4  4  4 2 2 2 | 0 2 2 2 1
------------------+-------+----------+----------------------+----------------------+----------
.. x. ..    ..    |  2  0 | 96  *  * |  1  1  1  1  0  0  0 | 1 1 1  1  1  1 0 0 0 | 1 1 1 1 0
oo3oo3oo *b3oo&#x |  1  1 |  * 24  *   0  0  0  8  0  0  0 | 0 0 0  4  4  4 0 0 0 | 0 2 2 2 0
.. .x ..    ..    |  0  2 |  *  * 96 |  0  0  0  1  1  1  1 | 0 0 0  1  1  1 1 1 1 | 0 1 1 1 1
------------------+-------+----------+----------------------+----------------------+----------
o.3x. ..    ..    |  3  0 |  3  0  0 | 32  *  *  *  *  *  * | 1 1 0  1  0  0 0 0 0 | 1 1 1 0 0
.. x.3o.    ..    |  3  0 |  3  0  0 |  * 32  *  *  *  *  * | 1 0 1  0  1  0 0 0 0 | 1 1 0 1 0
.. x. .. *b3o.    |  3  0 |  3  0  0 |  *  * 32  *  *  *  * | 0 1 1  0  0  1 0 0 0 | 1 0 1 1 0
.. xx ..    ..&#x |  2  2 |  1  2  1 |  *  *  * 96  *  *  * | 0 0 0  1  1  1 0 0 0 | 0 1 1 1 0
.o3.x ..    ..    |  0  3 |  0  0  3 |  *  *  *  * 32  *  * | 0 0 0  1  0  0 1 1 0 | 0 1 1 0 1
.. .x3.o    ..    |  0  3 |  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  3 |  *  *  *  *  *  * 32 | 0 0 0  0  0  1 0 1 1 | 0 0 1 1 1
------------------+-------+----------+----------------------+----------------------+----------
o.3x.3o.    ..      6  0 | 12  0  0 |  4  4  0  0  0  0  0 | 8 * *  *  *  * * * * | 1 1 0 0 0
o.3x. .. *b3o.      6  0 | 12  0  0 |  4  0  4  0  0  0  0 | * 8 *  *  *  * * * * | 1 0 1 0 0
.. x.3o. *b3o.      6  0 | 12  0  0 |  0  4  4  0  0  0  0 | * * 8  *  *  * * * * | 1 0 0 1 0
oo3xx ..    ..&#x   3  3 |  3  3  3 |  1  0  0  3  1  0  0 | * * * 32  *  * * * * | 0 1 1 0 0
.. xx3oo    ..&#x   3  3 |  3  3  3 |  0  1  0  3  0  1  0 | * * *  * 32  * * * * | 0 1 0 1 0
.. xx .. *b3oo&#x   3  3 |  3  3  3 |  0  0  1  3  0  0  1 | * * *  *  * 32 * * * | 0 0 1 1 0
.o3.x3.o    ..      0  6 |  0  0 12 |  0  0  0  0  4  4  0 | * * *  *  *  * 8 * * | 0 1 0 0 1
.o3.x .. *b3.o      0  6 |  0  0 12 |  0  0  0  0  4  0  4 | * * *  *  *  * * 8 * | 0 0 1 0 1
.. .x3.o *b3.o      0  6 |  0  0 12 |  0  0  0  0  0  4  4 | * * *  *  *  * * * 8 | 0 0 0 1 1
------------------+-------+----------+----------------------+----------------------+----------
o.3x.3o. *b3o.     24  0 | 96  0  0 | 32 32 32  0  0  0  0 | 8 8 8  0  0  0 0 0 0 | 1 * * * *
oo3xx3oo    ..&#x   6  6 | 12  6 12 |  4  4  0 12  4  4  0 | 1 0 0  4  4  0 1 0 0 | * 8 * * *
oo3xx .. *b3oo&#x   6  6 | 12  6 12 |  4  0  4 12  4  0  4 | 0 1 0  4  0  4 0 1 0 | * * 8 * *
.. xx3oo *b3oo&#x   6  6 | 12  6 12 |  0  4  4 12  0  4  4 | 0 0 1  0  4  4 0 0 1 | * * * 8 *
.o3.x3.o *b3.o      0 24 |  0  0 96 |  0  0  0  0 32 32 32 | 0 0 0  0  0  0 8 8 8 | * * * * 1

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