13-5 gyrochoron

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13-5 gyrochoron
Rank4
TypeIsotopic
Elements
Cells13 prodigonal antiprismatic symmetric elongated gyrobifastigia
Faces26 kites, 26 mirror-symmetric pentagons
Edges26+52
Vertices13+26
Vertex figure26 phyllic disphenoids, 13 tetragonal disphenoids
Measures (edge length 1)
Central density1
Related polytopes
Dual13-5 step prism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryS2(I2(13)-5)×2I, order 52
ConvexYes
NatureTame

The 13-5 gyrochoron, also known as the tridecachoron, is a convex isochoric polychoron and member of the gyrochoron family with 13 prodigonal antiprismatic symmetric elongated gyrobifastigia as cells. It is also the pentagonal funk prism.

Each cell of this polychoron has prodigonal antiprismatic symmetry, with 4 mirror-symmetric pentagons and 4 kites for faces.

Compared to other gyrochora with 13 cells, this polychoron has ionic doubled symmetry, because 13 is a factor of 52+1 = 26.

Isogonal derivatives[edit | edit source]

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

External links[edit | edit source]