Acronym ...
Name f3x5x,
variation of great rhombicosidodecahedron,
hull of quitdid
Circumradius sqrt[(77+33 sqrt(5))/8] = 4.341518
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between f . x and f3x (at f):   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
  • between f . x and x5x:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°
  • between f3x and x5x:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
Confer
uniform variant:
grid  
variations:
a3b5c   v3x5f   f3v5v   x3(-x)5f  

Incidence matrix according to Dynkin symbol

f3x5x

. . . | 120 |  1  1  1 |  1  1  1
------+-----+----------+---------
f . . |   2 | 60  *  * |  1  1  0
. x . |   2 |  * 60  * |  1  0  1
. . x |   2 |  *  * 60 |  0  1  1
------+-----+----------+---------
f3x . |   6 |  3  3  0 | 20  *  *
f . x |   4 |  2  0  2 |  * 30  *
. x5x |  10 |  0  5  5 |  *  * 12

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