Acronym 5,n-dip
Name pentagon - n-gon duoprism
Circumradius sqrt[(5+sqrt(5))/10+1/(4 sin2(π/n))]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Especially trapedip (n=3)   squipdip (n=4)   pedip (n=5)   phiddip (n=6)   podip (n=8)   padedip (n=10)  
Confer
general duoprisms:
n,m-dip  
External
links
hedrondude   wikipedia

Incidence matrix according to Dynkin symbol

x5o xno (n>2)

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

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