Acronym ...
Name q x5o,
variation of pentagonal prism
Circumradius sqrt[(10+sqrt(5))/10] = 1.106168
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Confer n-p   pip   f x5o   v x5o   u x5o   x v5o   f v5o  

using edge sizes x = 1 and q = sqrt(2) = 1.414214


Incidence matrix according to Dynkin symbol

q x5o

. . . | 10 | 1  2 | 2 1
------+----+------+----
q . . |  2 | 5  * | 2 0
. x . |  2 | * 10 | 1 1
------+----+------+----
q x . |  4 | 2  2 | 5 *
. x5o |  5 | 0  5 | * 2

xx5oo&#q   → height = sqrt(2) = 1.414214
({5} || {5})

o.5o.    | 5 * | 2 1 0 | 1 2 0
.o5.o    | * 5 | 0 1 2 | 0 2 1
---------+-----+-------+------
x. ..    | 2 0 | 5 * * | 1 1 0
oo5oo&#q | 1 1 | * 5 * | 0 2 0
.x ..    | 0 2 | * * 5 | 0 1 1
---------+-----+-------+------
x.5o.    | 5 0 | 5 0 0 | 1 * *
xx ..&#q | 2 2 | 1 2 1 | * 5 *
.x5.o    | 0 5 | 0 0 5 | * * 1

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