Acronym spidatip
Name small-prismate-pentachoron atop alternate truncated-pentachoron
Circumradius sqrt(13/8) = 1.274755
Confer
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

xx3xo3oo3ox&#x   → height = sqrt(2/5) = 0.632456
(tip || spid)

o.3o.3o.3o.    | 20  * |  1  3  3  0  0 |  3  3  3  6  3  0  0  0 | 3 1  6  3  3  3  1 0  0  0 0 | 1 3  3  1 1 0
.o3.o3.o3.o    |  * 20 |  0  0  3  3  3 |  0  0  3  3  6  3  6  3 | 0 0  3  6  1  3  3 1  3  3 1 | 0 1  3  3 1 1
---------------+-------+----------------+-------------------------+------------------------------+--------------
x. .. .. ..    |  2  0 | 10  *  *  *  * |  3  0  3  0  0  0  0  0 | 3 0  6  3  0  0  0 0  0  0 0 | 1 3  3  1 0 0
.. x. .. ..    |  2  0 |  * 30  *  *  * |  1  2  0  2  0  0  0  0 | 2 1  2  0  2  1  0 0  0  0 0 | 1 2  1  0 1 0
oo3oo3oo3oo&#x |  1  1 |  *  * 60  *  * |  0  0  1  2  2  0  0  0 | 0 0  2  2  1  2  1 0  0  0 0 | 0 1  2  1 1 0
.x .. .. ..    |  0  2 |  *  *  * 30  * |  0  0  1  0  0  2  2  0 | 0 0  2  2  0  0  0 1  2  1 0 | 0 1  2  1 0 1
.. .. .. .x    |  0  2 |  *  *  *  * 30 |  0  0  0  0  2  0  2  2 | 0 0  0  2  0  1  2 0  1  2 1 | 0 0  1  2 1 1
---------------+-------+----------------+-------------------------+------------------------------+--------------
x.3x. .. ..    |  6  0 |  3  3  0  0  0 | 10  *  *  *  *  *  *  * | 2 0  2  0  0  0  0 0  0  0 0 | 1 2  1  0 0 0
.. x.3o. ..    |  3  0 |  0  3  0  0  0 |  * 20  *  *  *  *  *  * | 1 1  0  0  1  0  0 0  0  0 0 | 1 1  0  0 1 0
xx .. .. ..&#x |  2  2 |  1  0  2  1  0 |  *  * 30  *  *  *  *  * | 0 0  2  2  0  0  0 0  0  0 0 | 0 1  2  1 0 0
.. xo .. ..&#x |  2  1 |  0  1  2  0  0 |  *  *  * 60  *  *  *  * | 0 0  1  0  1  1  0 0  0  0 0 | 0 1  1  0 1 0
.. .. .. ox&#x |  1  2 |  0  0  2  0  1 |  *  *  *  * 60  *  *  * | 0 0  0  1  0  1  1 0  0  0 0 | 0 0  1  1 1 0
.x3.o .. ..    |  0  3 |  0  0  0  3  0 |  *  *  *  *  * 20  *  * | 0 0  1  0  0  0  0 1  1  0 0 | 0 1  1  0 0 1
.x .. .. .x    |  0  4 |  0  0  0  2  2 |  *  *  *  *  *  * 30  * | 0 0  0  1  0  0  0 0  1  1 0 | 0 0  1  1 0 1
.. .. .o3.x    |  0  3 |  0  0  0  0  3 |  *  *  *  *  *  *  * 20 | 0 0  0  0  0  0  1 0  0  1 1 | 0 0  0  1 1 1
---------------+-------+----------------+-------------------------+------------------------------+--------------
x.3x.3o. ..     12  0 |  6 12  0  0  0 |  4  4  0  0  0  0  0  0 | 5 *  *  *  *  *  * *  *  * * | 1 1  0  0 0 0
.. x.3o.3o.      4  0 |  0  6  0  0  0 |  0  4  0  0  0  0  0  0 | * 5  *  *  *  *  * *  *  * * | 1 0  0  0 1 0
xx3xo .. ..&#x   6  3 |  3  3  6  3  0 |  1  0  3  3  0  1  0  0 | * * 20  *  *  *  * *  *  * * | 0 1  1  0 0 0
xx .. .. ox&#x   2  4 |  1  0  4  2  2 |  0  0  2  0  2  0  1  0 | * *  * 30  *  *  * *  *  * * | 0 0  1  1 0 0
.. xo3oo ..&#x   3  1 |  0  3  3  0  0 |  0  1  0  3  0  0  0  0 | * *  *  * 20  *  * *  *  * * | 0 1  0  0 1 0
.. xo .. ox&#x   2  2 |  0  1  4  0  1 |  0  0  0  2  2  0  0  0 | * *  *  *  * 30  * *  *  * * | 0 0  1  0 1 0
.. .. oo3ox&#x   1  3 |  0  0  3  0  3 |  0  0  0  0  3  0  0  1 | * *  *  *  *  * 20 *  *  * * | 0 0  0  1 1 0
.x3.o3.o ..      0  4 |  0  0  0  6  0 |  0  0  0  0  0  4  0  0 | * *  *  *  *  *  * 5  *  * * | 0 1  0  0 0 1
.x3.o .. .x      0  6 |  0  0  0  6  3 |  0  0  0  0  0  2  3  0 | * *  *  *  *  *  * * 10  * * | 0 0  1  0 0 1
.x .. .o3.x      0  6 |  0  0  0  3  6 |  0  0  0  0  0  0  3  2 | * *  *  *  *  *  * *  * 10 * | 0 0  0  1 0 1
.. .o3.o3.x      0  4 |  0  0  0  0  6 |  0  0  0  0  0  0  0  4 | * *  *  *  *  *  * *  *  * 5 | 0 0  0  0 1 1
---------------+-------+----------------+-------------------------+------------------------------+--------------
x.3x.3o.3o.     20  0 | 10 30  0  0  0 | 10 20  0  0  0  0  0  0 | 5 5  0  0  0  0  0 0  0  0 0 | 1 *  *  * * *
xx3xo3oo ..&#x  12  4 |  6 12 12  6  0 |  4  4  6 12  0  4  0  0 | 1 0  4  0  4  0  0 1  0  0 0 | * 5  *  * * *
xx3xo .. ox&#x   6  6 |  3  3 12  6  3 |  1  0  6  6  6  2  3  0 | 0 0  2  3  0  3  0 0  1  0 0 | * * 10  * * *
xx .. oo3ox&#x   2  6 |  1  0  6  3  6 |  0  0  3  0  6  0  3  2 | 0 0  0  3  0  0  2 0  0  1 0 | * *  * 10 * *
.. xo3oo3ox&#x   4  4 |  0  6 12  0  6 |  0  4  0 12 12  0  0  4 | 0 1  0  0  4  6  4 0  0  0 1 | * *  *  * 5 *
.x3.o3.o3.x      0 20 |  0  0  0 30 30 |  0  0  0  0  0 20 30 20 | 0 0  0  0  0  0  0 5 10 10 5 | * *  *  * * 1

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