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 Externallinks

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
```