Acronym penaspid
Name pentachoron atop small prismated decachoron,
pen-first rotunda of scad
Circumradius 1
Lace city
in approx. ASCII-art
  o   t  		-- o3o3o3x (pen)
         
T   C   t		-- x3o3o3x (spid)

where:
o - o3o3o (point)
t - x3o3o (tet)
C - x3o3x (co)
T - o3o3x (dual tet)
Confer
uniform relative:
scad  
general polytopal classes:
segmentotera  

Incidence matrix according to Dynkin symbol

xx3oo3oo3ox&#x   → heights = sqrt(3/5) = 0.774597
(pen || spid)

o..3o..3o..3o..    | 5  *   4  4  0  0 |  6 12  6  0  0  0 | 4 12 12  4 0  0  0 0 | 1 4  6  4 1 0
.o.3.o.3.o.3.o.    | * 20 |  0  1  3  3 |  0  3  3  3  6  3 | 0  3  6  3 1  3  3 1 | 0 1  3  3 1 1
-------------------+------+-------------+-------------------+----------------------+--------------
x.. ... ... ...    | 2  0 | 10  *  *  * |  3  3  0  0  0  0 | 3  6  3  0 0  0  0 0 | 1 3  3  1 0 0
oo.3oo.3oo.3oo.&#x | 1  1 |  * 20  *  * |  0  3  3  0  0  0 | 0  3  6  3 0  0  0 0 | 0 1  3  3 1 0
.x. ... ... ...    | 0  2 |  *  * 30  * |  0  1  0  2  2  0 | 0  2  2  0 1  2  1 0 | 0 1  2  1 0 1
... ... ... .x.    | 0  2 |  *  *  * 30 |  0  0  1  0  2  2 | 0  0  2  2 0  1  2 1 | 0 0  1  2 1 1
-------------------+------+-------------+-------------------+----------------------+--------------
x..3o.. ... ...    | 3  0 |  3  0  0  0 | 10  *  *  *  *  * | 2  2  0  0 0  0  0 0 | 1 2  1  0 0 0
xx. ... ... ...&#x | 2  2 |  1  2  1  0 |  * 30  *  *  *  * | 0  2  2  0 0  0  0 0 | 0 1  2  1 0 0
... ... ... ox.&#x | 1  2 |  0  2  0  1 |  *  * 30  *  *  * | 0  0  2  2 0  0  0 0 | 0 0  1  2 1 0
.x.3.o. ... ...    | 0  3 |  0  0  3  0 |  *  *  * 20  *  * | 0  1  0  0 1  1  0 0 | 0 1  1  0 0 1
.x. ... ... .x.    | 0  4 |  0  0  2  2 |  *  *  *  * 30  * | 0  0  1  0 0  1  1 0 | 0 0  1  1 0 1
... ... .o.3.x.    | 0  3 |  0  0  0  3 |  *  *  *  *  * 20 | 0  0  0  1 0  0  1 1 | 0 0  0  1 1 1
-------------------+------+-------------+-------------------+----------------------+--------------
x..3o..3o.. ...     4  0 |  6  0  0  0 |  4  0  0  0  0  0 | 5  *  *  * *  *  * * | 1 1  0  0 0 0
xx.3oo. ... ...&#x  3  3 |  3  3  3  0 |  1  3  0  1  0  0 | * 20  *  * *  *  * * | 0 1  1  0 0 0
xx. ... ... ox.&#x  2  4 |  1  4  2  2 |  0  2  2  0  1  0 | *  * 30  * *  *  * * | 0 0  1  1 0 0
... ... oo.3ox.&#x  1  3 |  0  3  0  3 |  0  0  3  0  0  1 | *  *  * 20 *  *  * * | 0 0  0  1 1 0
.x.3.o.3.o. ...     0  4 |  0  0  6  0 |  0  0  0  4  0  0 | *  *  *  * 5  *  * * | 0 1  0  0 0 1
.x.3.o. ... .x.     0  6 |  0  0  6  3 |  0  0  0  2  3  0 | *  *  *  * * 10  * * | 0 0  1  0 0 1
.x. ... .o.3.x.     0  6 |  0  0  3  6 |  0  0  0  0  3  2 | *  *  *  * *  * 10 * | 0 0  0  1 0 1
... .o.3.o.3.x.     0  4 |  0  0  0  6 |  0  0  0  0  0  4 | *  *  *  * *  *  * 5 | 0 0  0  0 1 1
-------------------+------+-------------+-------------------+----------------------+--------------
x..3o..3o..3o..     5  0 | 10  0  0  0 | 10  0  0  0  0  0 | 5  0  0  0 0  0  0 0 | 1 *  *  * * *
xx.3oo.3oo. ...&#x  4  4 |  6  4  6  0 |  4  6  0  4  0  0 | 1  4  0  0 1  0  0 0 | * 5  *  * * *
xx.3oo. ... ox.&#x  3  6 |  3  6  6  3 |  1  6  3  2  3  0 | 0  2  3  0 0  1  0 0 | * * 10  * * *
xx. ... oo.3ox.&#x  2  6 |  1  6  3  6 |  0  3  6  0  3  2 | 0  0  3  2 0  0  1 0 | * *  * 10 * *
... oo.3oo.3ox.&#x  1  4 |  0  4  0  6 |  0  0  6  0  0  4 | 0  0  0  4 0  0  0 1 | * *  *  * 5 *
.x.3.o.3.o.3.x.     0 20 |  0  0 30 30 |  0  0  0 20 30 20 | 0  0  0  0 5 10 10 5 | * *  *  * * 1

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