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[33]
General of army doe
Colonel of regiment (itself, even so not being locally convex)
Dihedral angles
(at margins)
  • between {3} and {3}:   arccos(1/3) = 70.528779°
Confer
related compounds:
ki  
general polytopal classes:
regular  
External
links
hedrondude   wikipedia   mathworld

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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