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.

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

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

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

External links edit