Acronym  e 
Name 
icosiicosahedron, compound of 10 tet 
Coxeter symbol  2{5,3}[10{3,3}]2{3,5} 
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Circumradius  sqrt(3/8) = 0.612372 
Inradius  1/sqrt(24) = 0.204124 
Vertex figure  2[3^{3}] 
General of army  doe 
Colonel of regiment  (itself, even so not being locally convex) 
Dihedral angles
(at margins) 

Confer  
External links 
The common intersection of the icosiicosahedron is a (scaled) ike. Moreover the icosiicosahedron is selfdual.
Both the triangles pairwise fall into coincident face planes, and the vertices coincide by pairs. So either both can be considered separately (type A); or vertices are identified, while triangles are kept separately (type B); or conversely, vertices are considered separately, while faces are considered as (rotated) 2trianglecompounds (type C); or finally both are considered combined (type D). Clearly types A and D are selfdual, while types B and C are anothers duals.
Finally e also is a compound of 2 (different handed) ki (type E).
(Type A) 40  3  3  1 ++++ 2  60  2  1 ++++ 3  3  40  1 ++++ ♦ 4  6  4  10
(Type B) 20  6  6  2 ++++ 2  60  2  1 ++++ 3  3  40  1 ++++ ♦ 4  6  4  10
(Type C) 40  3  3  1 ++++ 2  60  2  1 ++++ 6  6  20  2 ++++ ♦ 4  6  4  10
(Type D) 20  6  6  2 ++++ 2  60  2  1 ++++ 6  6  20  2 ++++ ♦ 4  6  4  10
(Type E) 40  3  3  1 ++++ 2  60  2  1 ++++ 3  3  40  1 ++++ ♦ 20  30  20  2
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