13-5 gyrochoron

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

Each cell of this polychoron has prodigonal antiprismatic symmetry, with 4 pentagonal and 4 tetragonal faces.

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

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Elongated gyrobifastigium (13): 13-5 step prism
 * Mirror-symmetric pentagon (26): Small 13-5 double gyrostep prism
 * Kite (26): 13-5 double step prism
 * Vertex (13): 13-5 step prism