Acronym	e
Name	icosiicosahedron, compound of 10 tet
Coxeter symbol	2{5,3}[10{3,3}]2{3,5}
	©   ©   ©
Circumradius	sqrt(3/8) = 0.612372
Inradius	1/sqrt(24) = 0.204124
Vertex figure	2[33]
General of army	doe
Colonel of regiment	(itself, although not being locally convex)
Admiral of fleet	ike
Dual	selfdual
Dihedral angles (at margins)	between {3} and {3}:   arccos(1/3) = 70.528779°
Confer	related compounds: ki   general polytopal classes: regular
External links

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) 2-triangle-compounds (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).

The edge-on picture obove shows that this compound does not have a mirror symmetry wrt. its mid-edge plane. Thence it is not flag transitive and thus not regular in this sense. Even though, it both has a regular solid for its hull (doe) and for its kernel (ike). Thence it is regular in the sense of Coxeter.

Incidence matrix

(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