Acronym spidaprip
Name spid atop prip,
spid-first monostratic cap of spat
Circumradius sqrt(7/2) = 1.870829
Lace city
in approx. ASCII-art
    x3o3o   x3o3x   o3o3x    	-- x3o3o3x (spid)
                             
                             
                             
x3x3o   x3x3x   u3o3x   x3o3x	-- x3x3o3x (prip)
Confer
uniform relative:
spat  
general polytopal classes:
segmentotera   lace simplices  

Incidence matrix according to Dynkin symbol

xx3oo3ox3xx&#xt   → height = sqrt(2/5) = 0.632456
(spid || prip)

o.3o.3o.3o.    | 20  * |  3  3  3  0  0  0 |  3  6  3  6  3  3  0  0  0  0  0 | 1  3  3 1  3  3  6  1  3 0  0  0 0 | 1 1  3  3 1 0
.o3.o3.o3.o    |  * 60 |  0  0  1  2  2  1 |  0  0  0  2  2  1  1  2  2  1  2 | 0  0  0 0  1  2  2  1  2 1  1  2 1 | 0 1  1  2 1 1
---------------+-------+-------------------+----------------------------------+------------------------------------+--------------
x. .. .. ..    |  2  0 | 30  *  *  *  *  * |  2  2  0  2  0  0  0  0  0  0  0 | 1  2  1 0  2  1  2  0  0 0  0  0 0 | 1 1  2  1 0 0
.. .. .. x.    |  2  0 |  * 30  *  *  *  * |  0  2  2  0  0  1  0  0  0  0  0 | 0  1  2 1  0  0  2  0  2 0  0  0 0 | 1 0  1  2 1 0
oo3oo3oo3oo&#x |  1  1 |  *  * 60  *  *  * |  0  0  0  2  2  1  0  0  0  0  0 | 0  0  0 0  1  2  2  1  2 0  0  0 0 | 0 1  1  2 1 0
.x .. .. ..    |  0  2 |  *  *  * 60  *  * |  0  0  0  1  0  0  1  1  1  0  0 | 0  0  0 0  1  1  1  0  0 1  1  1 0 | 0 1  1  1 0 1
.. .. .x ..    |  0  2 |  *  *  *  * 60  * |  0  0  0  0  1  0  0  1  0  1  1 | 0  0  0 0  0  1  0  1  1 1  0  1 1 | 0 1  0  1 1 1
.. .. .. .x    |  0  2 |  *  *  *  *  * 30 |  0  0  0  0  0  1  0  0  2  0  2 | 0  0  0 0  0  0  2  0  2 0  1  2 1 | 0 0  1  2 1 1
---------------+-------+-------------------+----------------------------------+------------------------------------+--------------
x.3o. .. ..    |  3  0 |  3  0  0  0  0  0 | 20  *  *  *  *  *  *  *  *  *  * | 1  1  0 0  1  0  0  0  0 0  0  0 0 | 1 1  1  0 0 0
x. .. .. x.    |  4  0 |  2  2  0  0  0  0 |  * 30  *  *  *  *  *  *  *  *  * | 0  1  1 0  0  0  1  0  0 0  0  0 0 | 1 0  1  1 0 0
.. .. o.3x.    |  3  0 |  0  3  0  0  0  0 |  *  * 20  *  *  *  *  *  *  *  * | 0  0  1 1  0  0  0  0  1 0  0  0 0 | 1 0  0  1 1 0
xx .. .. ..&#x |  2  2 |  1  0  2  1  0  0 |  *  *  * 60  *  *  *  *  *  *  * | 0  0  0 0  1  1  1  0  0 0  0  0 0 | 0 1  1  1 0 0
.. .. ox ..&#x |  1  2 |  0  0  2  0  1  0 |  *  *  *  * 60  *  *  *  *  *  * | 0  0  0 0  0  1  0  1  1 0  0  0 0 | 0 1  0  1 1 0
.. .. .. xx&#x |  2  2 |  0  1  2  0  0  1 |  *  *  *  *  * 30  *  *  *  *  * | 0  0  0 0  0  0  2  0  2 0  0  0 0 | 0 0  1  2 1 0
.x3.o .. ..    |  0  3 |  0  0  0  3  0  0 |  *  *  *  *  *  * 20  *  *  *  * | 0  0  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  0 |  *  *  *  *  *  *  * 30  *  *  * | 0  0  0 0  0  1  0  0  0 1  0  1 0 | 0 1  0  1 0 1
.x .. .. .x    |  0  4 |  0  0  0  2  0  2 |  *  *  *  *  *  *  *  * 30  *  * | 0  0  0 0  0  0  1  0  0 0  1  1 0 | 0 0  1  1 0 1
.. .o3.x ..    |  0  3 |  0  0  0  0  3  0 |  *  *  *  *  *  *  *  *  * 20  * | 0  0  0 0  0  0  0  1  0 1  0  0 1 | 0 1  0  0 1 1
.. .. .x3.x    |  0  6 |  0  0  0  0  3  3 |  *  *  *  *  *  *  *  *  *  * 20 | 0  0  0 0  0  0  0  0  1 0  0  1 1 | 0 0  0  1 1 1
---------------+-------+-------------------+----------------------------------+------------------------------------+--------------
x.3o.3o. ..      4  0 |  6  0  0  0  0  0 |  4  0  0  0  0  0  0  0  0  0  0 | 5  *  * *  *  *  *  *  * *  *  * * | 1 1  0  0 0 0
x.3o. .. x.      6  0 |  6  3  0  0  0  0 |  2  3  0  0  0  0  0  0  0  0  0 | * 10  * *  *  *  *  *  * *  *  * * | 1 0  1  0 0 0
x. .. o.3x.      6  0 |  3  6  0  0  0  0 |  0  3  2  0  0  0  0  0  0  0  0 | *  * 10 *  *  *  *  *  * *  *  * * | 1 0  0  1 0 0
.. o.3o.3x.      4  0 |  0  6  0  0  0  0 |  0  0  4  0  0  0  0  0  0  0  0 | *  *  * 5  *  *  *  *  * *  *  * * | 1 0  0  0 1 0
xx3oo .. ..&#x   3  3 |  3  0  3  3  0  0 |  1  0  0  3  0  0  1  0  0  0  0 | *  *  * * 20  *  *  *  * *  *  * * | 0 1  1  0 0 0
xx .. ox ..&#x   2  4 |  1  0  4  2  2  0 |  0  0  0  2  2  0  0  1  0  0  0 | *  *  * *  * 30  *  *  * *  *  * * | 0 1  0  1 0 0
xx .. .. xx&#x   4  4 |  2  2  4  2  0  2 |  0  1  0  2  0  2  0  0  1  0  0 | *  *  * *  *  * 30  *  * *  *  * * | 0 0  1  1 0 0
.. oo3ox ..&#x   1  3 |  0  0  3  0  3  0 |  0  0  0  0  3  0  0  0  0  1  0 | *  *  * *  *  *  * 20  * *  *  * * | 0 1  0  0 1 0
.. .. ox3xx&#x   3  6 |  0  3  6  0  3  3 |  0  0  1  0  3  3  0  0  0  0  1 | *  *  * *  *  *  *  * 20 *  *  * * | 0 0  0  1 1 0
.x3.o3.x ..      0 12 |  0  0  0 12 12  0 |  0  0  0  0  0  0  4  6  0  4  0 | *  *  * *  *  *  *  *  * 5  *  * * | 0 1  0  0 0 1
.x3.o .. .x      0  6 |  0  0  0  6  0  3 |  0  0  0  0  0  0  2  0  3  0  0 | *  *  * *  *  *  *  *  * * 10  * * | 0 0  1  0 0 1
.x .. .x3.x      0 12 |  0  0  0  6  6  6 |  0  0  0  0  0  0  0  3  3  0  2 | *  *  * *  *  *  *  *  * *  * 10 * | 0 0  0  1 0 1
.. .o3.x3.x      0 12 |  0  0  0  0 12  6 |  0  0  0  0  0  0  0  0  0  4  4 | *  *  * *  *  *  *  *  * *  *  * 5 | 0 0  0  0 1 1
---------------+-------+-------------------+----------------------------------+------------------------------------+--------------
x.3o.3o.3x.     20  0 | 30 30  0  0  0  0 | 20 30 20  0  0  0  0  0  0  0  0 | 5 10 10 5  0  0  0  0  0 0  0  0 0 | 1 *  *  * * *
xx3oo3ox ..&#x   4 12 |  6  0 12 12 12  0 |  4  0  0 12 12  0  4  6  0  4  0 | 1  0  0 0  4  6  0  4  0 1  0  0 0 | * 5  *  * * *
xx3oo .. xx&#x   6  6 |  6  3  6  6  0  3 |  2  3  0  6  0  3  2  0  3  0  0 | 0  1  0 0  2  0  3  0  0 0  1  0 0 | * * 10  * * *
xx .. ox3xx&#x   6 12 |  3  6 12  6  6  6 |  0  3  2  6  6  6  0  3  3  0  2 | 0  0  1 0  0  3  3  0  2 0  0  1 0 | * *  * 10 * *
.. oo3ox3xx&#x   4 12 |  0  6 12  0 12  6 |  0  0  4  0 12  6  0  0  0  4  4 | 0  0  0 1  0  0  0  4  4 0  0  0 1 | * *  *  * 5 *
.x3.o3.x3.x      0 60 |  0  0  0 60 60 30 |  0  0  0  0  0  0 20 30 30 20 20 | 0  0  0 0  0  0  0  0  0 5 10 10 5 | * *  *  * * 1

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