Augmented sphenocorona

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Augmented sphenocorona
Rank3
TypeCRF
Notation
Bowers style acronymAuwaco
Elements
Faces1+1+1+1+2+2+2+2+2+2 triangles, 1 square
Edges1+1+1+1+2+2+2+2+2+2+2+2+2+2+2
Vertices1+1+1+2+2+2+2
Vertex figures1+1+2+2 pentagons, edge length 1
 2 trapezoids, edge lengths 1, 1, 1, 2
 2 irregular pentagons, edge lengths 1, 1, 1, 1, 2
 1 square, edge length 1
Measures (edge length 1)
Volume
Central density1
Number of external pieces17
Level of complexity52
Related polytopes
ArmyAuwaco
RegimentAuwaco
DualOrder-4 monotruncated order-5 truncated bi-apiculated tetrahedron
ConjugateAugmented sphenocorona
Abstract & topological properties
Flag count104
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA1×I×I, order 2
ConvexYes
NatureTame

The augmented sphenocorona is one of the 92 Johnson solids (J87). It consists of 1+1+1+1+2+2+2+2+2+2 triangles and 1 square. It can be constructed by attaching a square pyramid to one of the square faces of the sphenocorona.

Coordinates[edit | edit source]

Coordinates for the vertices of an sphenocorona with unit edge length are given by:

  • ,
  • ,
  • ,
  • ,
  • .

where k  ≈ 0.85273 is the smallest positive root of the quartic polynomial:

This root can also be given as:

External links[edit | edit source]