Acronym tipagrip
Name tip atop grip
Circumradius sqrt(37/8) = 2.150581
Confer
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

oo3ox3xx3xx&#x   → height = sqrt(2/5) = 0.632455
(tip || grip)

o.3o.3o.3o.    | 20  * |  3  1  3  0  0  0 |  3  3  3  3  3  0  0  0  0 | 1 3  1  3  3  3 0  0 0 | 1 1  1 3 0
.o3.o3.o3.o    |  * 60 |  0  0  1  2  1  1 |  0  0  2  1  1  1  2  2  1 | 0 0  1  2  2  1 1  1 2 | 0 1  1 2 1
---------------+-------+-------------------+----------------------------+------------------------+-----------
.. .. x. ..    |  2  0 | 30  *  *  *  *  * |  2  1  0  1  0  0  0  0  0 | 1 2  0  2  0  1 0  0 0 | 1 1  0 2 0
.. .. .. x.    |  2  0 |  * 10  *  *  *  * |  0  3  0  0  3  0  0  0  0 | 0 3  0  0  3  3 0  0 0 | 1 0  1 3 0
oo3oo3oo3oo&#x |  1  1 |  *  * 60  *  *  * |  0  0  2  1  1  0  0  0  0 | 0 0  1  2  2  1 0  0 0 | 0 1  1 2 0
.. .x .. ..    |  0  2 |  *  *  * 60  *  * |  0  0  1  0  0  1  1  1  0 | 0 0  1  1  1  1 0  0 0 | 0 1  1 1 1
.. .. .x ..    |  0  2 |  *  *  *  * 30  * |  0  0  0  1  0  0  2  0  1 | 0 0  0  2  0  1 1  0 2 | 0 1  0 2 1
.. .. .. .x    |  0  2 |  *  *  *  *  * 30 |  0  0  0  0  1  0  0  2  1 | 0 0  0  0  2  1 0  1 2 | 0 0  1 2 1
---------------+-------+-------------------+----------------------------+------------------------+-----------
.. o.3x. ..    |  3  0 |  3  0  0  0  0  0 | 20  *  *  *  *  *  *  *  * | 1 1  0  1  0  0 0  0 0 | 1 1  0 1 0
.. .. x.3x.    |  6  0 |  3  3  0  0  0  0 |  * 10  *  *  *  *  *  *  * | 0 2  0  0  0  1 0  0 0 | 1 0  0 2 0
.. ox .. ..&#x |  1  2 |  0  0  2  1  0  0 |  *  * 60  *  *  *  *  *  * | 0 0  1  1  1  0 0  0 0 | 0 1  1 1 0
.. .. xx ..&#x |  2  2 |  1  0  2  0  1  0 |  *  *  * 30  *  *  *  *  * | 0 0  0  2  0  1 0  0 0 | 0 1  0 2 0
.. .. .. xx&#x |  2  2 |  0  1  2  0  0  1 |  *  *  *  * 30  *  *  *  * | 0 0  0  0  2  1 0  0 0 | 0 0  1 2 0
.o3.x .. ..    |  0  3 |  0  0  0  3  0  0 |  *  *  *  *  * 20  *  *  * | 0 0  1  0  0  0 1  1 0 | 0 1  1 0 1
.. .x3.x ..    |  0  6 |  0  0  0  3  3  0 |  *  *  *  *  *  * 20  *  * | 0 0  0  1  0  0 1  0 1 | 0 1  0 1 1
.. .x .. .x    |  0  4 |  0  0  0  2  0  2 |  *  *  *  *  *  *  * 30  * | 0 0  0  0  1  0 0  1 1 | 0 0  1 1 1
.. .. .x3.x    |  0  6 |  0  0  0  0  3  3 |  *  *  *  *  *  *  *  * 10 | 0 0  0  0  0  1 0  0 2 | 0 0  0 2 1
---------------+-------+-------------------+----------------------------+------------------------+-----------
o.3o.3x. ..      4  0 |  6  0  0  0  0  0 |  4  0  0  0  0  0  0  0  0 | 5 *  *  *  *  * *  * * | 1 1  0 0 0
.. o.3x.3x.     12  0 | 12  6  0  0  0  0 |  4  4  0  0  0  0  0  0  0 | * 5  *  *  *  * *  * * | 1 0  0 1 0
oo3ox .. ..&#x   1  3 |  0  0  3  3  0  0 |  0  0  3  0  0  1  0  0  0 | * * 20  *  *  * *  * * | 0 1  1 0 0
.. ox3xx ..&#x   3  6 |  3  0  6  3  3  0 |  1  0  3  3  0  0  1  0  0 | * *  * 20  *  * *  * * | 0 1  0 1 0
.. ox .. xx&#x   2  4 |  0  1  4  2  0  2 |  0  0  2  0  2  0  0  1  0 | * *  *  * 30  * *  * * | 0 0  1 1 0
.. .. xx3xx&#x   6  6 |  3  3  6  0  3  3 |  0  1  0  3  3  0  0  0  1 | * *  *  *  * 10 *  * * | 0 0  0 2 0
.o3.x3.x ..      0 12 |  0  0  0 12  6  0 |  0  0  0  0  0  4  4  0  0 | * *  *  *  *  * 5  * * | 0 1  0 0 1
.o3.x .. .x      0  6 |  0  0  0  6  0  3 |  0  0  0  0  0  2  0  3  0 | * *  *  *  *  * * 10 * | 0 0  1 0 1
.. .x3.x3.x      0 24 |  0  0  0 12 12 12 |  0  0  0  0  0  0  4  6  4 | * *  *  *  *  * *  * 5 | 0 0  0 1 1
---------------+-------+-------------------+----------------------------+------------------------+-----------
o.3o.3x.3x.     20  0 | 30 10  0  0  0  0 | 20 10  0  0  0  0  0  0  0 | 5 5  0  0  0  0 0  0 0 | 1 *  * * *
oo3ox3xx ..&#x   4 12 |  6  0 12 12  6  0 |  4  0 12  6  0  4  4  0  0 | 1 0  4  4  0  0 1  0 0 | * 5  * * *
oo3ox .. xx&#x   2  6 |  0  1  6  6  0  3 |  0  0  6  0  3  2  0  3  0 | 0 0  2  0  3  0 0  1 0 | * * 10 * *
.. ox3xx3xx&#x  12 24 | 12  6 24 12 12 12 |  4  4 12 12 12  0  4  6  4 | 0 1  0  4  6  4 0  0 1 | * *  * 5 *
.o3.x3.x3.x      0 60 |  0  0  0 60 30 30 |  0  0  0  0  0 20 20 30 10 | 0 0  0  0  0  0 5 10 5 | * *  * * 1

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