Acronym ...
Name f x5o,
variation of pentagonal prism
Circumradius sqrt[(35+9 sqrt(5))/40] = 1.173932
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Confer
general prisms:
n-p  
uniform variant:
pip  
variations:
q x5o   v x5o   u x5o   x v5o   f v5o  

Incidence matrix according to Dynkin symbol

f x5o

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

xx5oo&#f   → height = (1+sqrt(5))/2 = 1.618034
({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&#f | 1 1 | * 5 * | 0 2 0
.x ..    | 0 2 | * * 5 | 0 1 1
---------+-----+-------+------
x.5o.    | 5 0 | 5 0 0 | 1 * *
xx ..&#f | 2 2 | 1 2 1 | * 5 *
.x5.o    | 0 5 | 0 0 5 | * * 1

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