Acronym taccup
Name triacontiditeron prism,
vertex figure of rez
Circumradius sqrt(3)/2 = 0.866025
Coordinates (1/sqrt(2), 0, 0, 0, 0, 1/2)   & all permutations in all but last coord., all changes of sign
Confer
general polytopal classes:
segmentopeta  

Incidence matrix according to Dynkin symbol

x x3o3o3o4o

. . . . . . | 20 |  1  8 |  8  24 | 24  32 | 32 16 | 16 1
------------+----+-------+--------+--------+-------+-----
x . . . . . |  2 | 10  *   8   0 | 24   0 | 32  0 | 16 0
. x . . . . |  2 |  * 80 |  1   6 |  6  12 | 12  8 |  8 1
------------+----+-------+--------+--------+-------+-----
x x . . . . |  4 |  2  2 | 40   *   6   0 | 12  0 |  8 0
. x3o . . . |  3 |  0  3 |  * 160 |  1   4 |  4  4 |  4 1
------------+----+-------+--------+--------+-------+-----
x x3o . . .   6 |  3  6 |  3   2 | 80   * |  4  0 |  4 0
. x3o3o . .   4 |  0  6 |  0   4 |  * 160 |  1  2 |  2 1
------------+----+-------+--------+--------+-------+-----
x x3o3o . .   8 |  4 12 |  6   8 |  4   2 | 80  * |  2 0
. x3o3o3o .   5 |  0 10 |  0  10 |  0   5 |  * 64 |  1 1
------------+----+-------+--------+--------+-------+-----
x x3o3o3o .  10 |  5 20 | 10  20 | 10  10 |  5  2 | 32 *
. x3o3o3o4o  10 |  0 40 |  0  80 |  0  80 |  0 32 |  * 2

x o3o3o *c3o3x

. . . .    . . | 20 |  1  8 |  8  24 | 24  32 | 32  8  8 |  8  8 1
---------------+----+-------+--------+--------+----------+--------
x . . .    . . |  2 | 10  *   8   0 | 24   0 | 32  0  0 |  8  8 0
. . . .    . x |  2 |  * 80 |  1   6 |  6  12 | 12  4  4 |  4  4 1
---------------+----+-------+--------+--------+----------+--------
x . . .    . x |  4 |  2  2 | 40   *   6   0 | 12  0  0 |  4  4 0
. . . .    o3x |  3 |  0  3 |  * 160 |  1   4 |  4  2  2 |  2  2 1
---------------+----+-------+--------+--------+----------+--------
x . . .    o3x   6 |  3  6 |  3   2 | 80   * |  4  0  0 |  2  2 0
. . o . *c3o3x   4 |  0  6 |  0   4 |  * 160 |  1  1  1 |  1  1 1
---------------+----+-------+--------+--------+----------+--------
x . o . *c3o3x   8 |  4 12 |  6   8 |  4   2 | 80  *  * |  1  1 0
. o3o . *c3o3x   5 |  0 10 |  0  10 |  0   5 |  * 32  * |  1  0 1
. . o3o *c3o3x   5 |  0 10 |  0  10 |  0   5 |  *  * 32 |  0  1 1
---------------+----+-------+--------+--------+----------+--------
x o3o . *c3o3x  10 |  5 20 | 10  20 | 10  10 |  5  2  0 | 16  * *
x . o3o *c3o3x  10 |  5 20 | 10  20 | 10  10 |  5  0  2 |  * 16 *
. o3o3o *c3o3x  10 |  0 40 |  0  80 |  0  80 |  0 16 16 |  *  * 2

xx3oo3oo3oo4oo&#x   → height = 1
(tac || tac)

o.3o.3o.3o.4o.    | 10  * |  8  1  0 | 12  8  0 | 32 24  0 | 16 32  0 | 1 16 0
.o3.o3.o3.o4.o    |  * 10 |  0  1  8 |  0  8 12 |  0 24 32 |  0 32 16 | 0 16 1
------------------+-------+----------+----------+----------+----------+-------
x. .. .. .. ..    |  2  0 | 40  *  * |  6  1  0 | 12  6  0 |  8 12  0 | 1  8 0
oo3oo3oo3oo4oo&#x |  1  1 |  * 10  *   0  8  0 |  0 24  0 |  0 32  0 | 0 16 0
.x .. .. .. ..    |  0  2 |  *  * 40 |  0  1  6 |  0  6 12 |  0 12  8 | 0  8 1
------------------+-------+----------+----------+----------+----------+-------
x.3o. .. .. ..    |  3  0 |  3  0  0 | 80  *  * |  4  1  0 |  4  4  0 | 1  4 0
xx .. .. .. ..&#x |  2  2 |  1  2  1 |  * 40  *   0  6  0 |  0 12  0 | 0  8 0
.x3.o .. .. ..    |  0  3 |  0  0  3 |  *  * 80 |  0  1  4 |  0  4  4 | 0  4 1
------------------+-------+----------+----------+----------+----------+-------
x.3o.3o. .. ..      4  0 |  6  0  0 |  4  0  0 | 80  *  * |  2  1  0 | 1  2 0
xx3oo .. .. ..&#x   3  3 |  3  3  3 |  1  3  1 |  * 80  * |  0  4  0 | 0  4 0
.x3.o3.o .. ..      0  4 |  0  0  6 |  0  0  4 |  *  * 80 |  0  1  2 | 0  2 1
------------------+-------+----------+----------+----------+----------+-------
x.3o.3o.3o. ..      5  0 | 10  0  0 | 10  0  0 |  5  0  0 | 32  *  * | 1  1 0
xx3oo3oo .. ..&#x   4  4 |  6  4  6 |  4  6  4 |  1  4  1 |  * 80  * | 0  2 0
.x3.o3.o3.o ..      0  5 |  0  0 10 |  0  0 10 |  0  0  5 |  *  * 32 | 0  1 1
------------------+-------+----------+----------+----------+----------+-------
x.3o.3o.3o.4o.     10  0 | 40  0  0 | 80  0  0 | 80  0  0 | 32  0  0 | 1  * *
xx3oo3oo3oo ..&#x   5  5 | 10  5 10 | 10 10 10 |  5 10  5 |  1  5  1 | * 32 *
.x3.o3.o3.o4.o      0 10 |  0  0 40 |  0  0 80 |  0  0 80 |  0  0 32 | *  * 1

oo3oo3oo *b3oo3xx&#x   → height = 1
(tac || tac)

o.3o.3o. *b3o.3o.    | 10  * |  8  1  0 | 24  8  0 | 32 24  0 |  8  8 32  0  0 | 1  8  8 0
.o3.o3.o *b3.o3.o    |  * 10 |  0  1  8 |  0  8 24 |  0 24 32 |  0  0 32  8  8 | 0  8  8 1
---------------------+-------+----------+----------+----------+----------------+----------
.. .. ..    .. x.    |  2  0 | 40  *  * |  6  1  0 | 12  6  0 |  4  4 12  0  0 | 1  4  4 0
oo3oo3oo *b3oo3oo&#x |  1  1 |  * 10  *   0  8  0 |  0 24  0 |  0  0 32  0  0 | 0  8  8 0
.. .. ..    .. .x    |  0  2 |  *  * 40 |  0  1  6 |  0  6 12 |  0  0 12  4  4 | 0  4  4 1
---------------------+-------+----------+----------+----------+----------------+----------
.. .. ..    o.3x.    |  3  0 |  3  0  0 | 80  *  * |  4  1  0 |  2  2  4  0  0 | 1  2  2 0
.. .. ..    .. xx&#x |  2  2 |  1  2  1 |  * 40  *   0  6  0 |  0  0 12  0  0 | 0  4  4 0
.. .. ..    .o3.x    |  0  3 |  0  0  3 |  *  * 80 |  0  1  4 |  0  0  4  2  2 | 0  2  2 1
---------------------+-------+----------+----------+----------+----------------+----------
.. o. .. *b3o.3x.      4  0 |  6  0  0 |  4  0  0 | 80  *  * |  1  1  1  0  0 | 1  1  1 0
.. .. ..    oo3xx&#x   3  3 |  3  3  3 |  1  3  1 |  * 80  * |  0  0  4  0  0 | 0  2  2 0
.. .o .. *b3.o3.x      0  4 |  0  0  6 |  0  0  4 |  *  * 80 |  0  0  1  1  1 | 0  1  1 1
---------------------+-------+----------+----------+----------+----------------+----------
o.3o. .. *b3o.3x.      5  0 | 10  0  0 | 10  0  0 |  5  0  0 | 16  *  *  *  * | 1  1  0 0
.. o.3o. *b3o.3x.      5  0 | 10  0  0 | 10  0  0 |  5  0  0 |  * 16  *  *  * | 1  0  1 0
.. oo .. *b3oo3xx&#x   4  4 |  6  4  6 |  4  6  4 |  1  4  1 |  *  * 80  *  * | 0  1  1 0
.o3.o .. *b3.o3.x      0  5 |  0  0 10 |  0  0 10 |  0  0  5 |  *  *  * 16  * | 0  1  0 1
.. .o3.o *b3.o3.x      0  5 |  0  0 10 |  0  0 10 |  0  0  5 |  *  *  *  * 16 | 0  0  1 1
---------------------+-------+----------+----------+----------+----------------+----------
o.3o.3o. *b3o.3x.     10  0 | 40  0  0 | 80  0  0 | 80  0  0 | 16 16  0  0  0 | 1  *  * *
oo3oo .. *b3oo3xx&#x   5  5 | 10  5 10 | 10 10 10 |  5 10  5 |  1  0  5  1  0 | * 16  * *
.. oo3oo *b3oo3xx&#x   5  5 | 10  5 10 | 10 10 10 |  5 10  5 |  0  1  5  0  1 | *  * 16 *
.o3.o3.o *b3.o3.x      0 10 |  0  0 40 |  0  0 80 |  0  0 80 |  0  0  0 16 16 | *  *  * 1

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