Bidecachoron

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Bidecachoron
Rank4
TypeNoble
Notation
Bowers style acronymBideca
Coxeter diagramo3m3m3o ()
Elements
Cells30 tetragonal disphenoids
Faces60 isosceles triangles
Edges20+20
Vertices10
Vertex figureTriakis tetrahedron
Measures (based on two pentachora of edge length 1)
Edge lengthsLacing edges (20):
 Edges of pentachora (20): 1
Circumradius
Inradius
Dichoral angle
Central density1
Related polytopes
ArmyBideca
RegimentBideca
DualDecachoron
Abstract & topological properties
Flag count720
Euler characteristic0
OrientableYes
Properties
SymmetryA4×2, order 240
ConvexYes
NatureTame

The bidecachoron or bideca, also known as the tetradisphenoidal triacontachoron, is a convex noble polychoron with 30 tetragonal disphenoids as cells. 12 cells join at each vertex, with the vertex figure being a triakis tetrahedron. It can be constructed as the convex hull of a pentachoron and its central inversion (or, equivalently, its dual). It is also the 10-3 step prism.

The ratio between the longest and shortest edges is 1: ≈ 1:1.29099.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a bidecachoron, based on two pentachora of edge length 1, centered at the origin, are given by:

  • ,
  • ,
  • ,
  • .

Variations[edit | edit source]

The bidecachoron has a number of variants that remain either isotopic or isogonal:

Isogonal derivatives[edit | edit source]

Substitution by vertices of these following elements will produce these convex isogonal polychora:

External links[edit | edit source]