12-4 gyrochoron

The 12-4 gyrochoron, also known as the trigon tetracoil, is a convex isochoric polychoron and member of the gyrochoron family with 12 tetragonal antiwedges as cells.

Each cell of this polychoron has bilateral symmetry, with 2 kites and 4 isosceles triangles for faces.

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Tetragonal antiwedge (12): 12-4 step prism
 * Kite (12): 12-4 step prism
 * Isosceles triangle (12): 12-4 step prism
 * Edge (12): 12-4 step prism
 * Edge (24): 24-4 step prism
 * Vertex (12): 12-4 step prism