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, even so not being locally convex) Confer related compounds: ki   general polytopal classes: regular Externallinks

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) 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).

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

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