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, 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
hedrondude   wikipedia   polytopewiki   mathworld

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

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