Acronym rid
Name rectified icosidodecahedron,
variation of small rhombicosidodecahedron
Circumradius sqrt[5+2 sqrt(5)] = 3.077684
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between x3o and x . f:   arccos(-(1+sqrt(5))/sqrt(12)) = 159.094843°
  • between x . f and o5f:   arccos(-sqrt[(5+sqrt(5))/10]) = 148.282526°
Face vector 60, 120, 62
Confer
uniform variant:
srid  
variations:
a3b5c   q3o5x   f3o5x   v3o5f  
ambification pre-image:
id  

Measures are using edge sizes x = 1 and f = (1+sqrt(5))/2 = 1.618034.

Rectification wrt. a non-regular polytope is meant to be the singular instance of truncations on all vertices at such a depth that the hyperplane intersections on the former edges will coincide (provided such a choice exists). Within the specific case of id all edges belong to a single orbit of symmetry, i.e. rectification clearly is applicable, without any recourse to Conway's ambification (chosing the former edge centers generally).


Incidence matrix according to Dynkin symbol

x3o5f

. . . | 60 |  2  2 |  1  2  1
------+----+-------+---------
x . . |  2 | 60  * |  1  1  0
. . f |  2 |  * 60 |  0  1  1
------+----+-------+---------
x3o . |  3 |  3  0 | 20  *  *
x . f |  4 |  2  2 |  * 30  *
. o5f |  5 |  0  5 |  *  * 12

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