Acronym ...
Name x v5o,
variation of pentagonal prism,
vertex figure of rigfix
Circumradius sqrt[(15-2 sqrt(5))/20] = 0.725530
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Confer n-p   pip   q x5o   f x5o   v x5o   u x5o   f v5o  

Incidence matrix according to Dynkin symbol

x v5o

. . . | 10 | 1  2 | 2 1
------+----+------+----
x . . |  2 | 5  * | 2 0
. v . |  2 | * 10 | 1 1
------+----+------+----
x v . |  4 | 2  2 | 5 *
. v5o |  5 | 0  5 | * 2

vv5oo&#x   → height = 1
(v-{5} || v-{5})

o.5o.    | 5 * | 2 1 0 | 1 2 0
.o5.o    | * 5 | 0 1 2 | 0 2 1
---------+-----+-------+------
v. ..    | 2 0 | 5 * * | 1 1 0
oo5oo&#x | 1 1 | * 5 * | 0 2 0
.v ..    | 0 2 | * * 5 | 0 1 1
---------+-----+-------+------
v.5o.    | 5 0 | 5 0 0 | 1 * *
vv ..&#x | 2 2 | 1 2 1 | * 5 *
.v5.o    | 0 5 | 0 0 5 | * * 1

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