Rectified small prismatodecachoron

The rectified small prismatodecachoron or respid is a convex isogonal polychoron that consists of 10 octahedra, 20 rectified triangular prisms, and 20 triangular antiprisms. 1 octahedron, 3 rectified triangular prisms, and 2 triangular antiprisms join at each vertex. It can be formed by rectifying the small prismatodecachoron.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the small rhombated pentachoron, where the edges of the octahedra are half the length of the other edges. It is one of five polychora (and two transitional cases) formed from two small rhombated pentachora, and is the transitional point between the small birhombatodecachoron and medial birhombatodecachoron.

The ratio between the longest and shortest edges is 1:$$\sqrt2$$ ≈ 1:1.41421.