Acronym	arie
Name	antirhombicosicosahedron, compound of 5 co
	© ©   ©
Circumradius	1
Vertex figure	[(3,4)2]
Dihedral angles (at margins)	between {3} and {4}:   arccos[-1/sqrt(3)] = 125.264390°
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Triangles pairwise fall into coincident face planes. So either they can be considered separately (type A); or they are considered as (rotated) 2-triangle-compounds (type B).

The second pic shows the cyan 5-fold rotational axis on a single co component and the respective orthogonal rotation plane. Note that the green edge intersection centers together with the red square normal provide 10 equiangular directions. (An according proof eg. is provided in that appendix.)

Incidence matrix

(Type A)

  60 |   4 |  2  2 || 1
-----+-----+-------++--
   2 | 120 |  1  1 || 1
-----+-----+-------++--
   3 |   3 | 40  * || 1
   4 |   4 |  * 30 || 1
-----+-----+-------++--
♦ 12 |  24 |  8  6 || 5

(Type B)

  60 |   4 |  2  2 || 1
-----+-----+-------++--
   2 | 120 |  1  1 || 1
-----+-----+-------++--
   6 |   6 | 20  * || 2
   4 |   4 |  * 30 || 1
-----+-----+-------++--
♦ 12 |  24 |  8  6 || 5