Bidecachoron

The bidecachoron or bideca, also known as the tetradisphenoidal triacontachoron, is a convex noble polychoron with 30 tetragonal disphenoids as cells. It is also the 10-3 step prism.

It is also the convex hull of a pentachoron and its central inversion.

The ratio between the longest and shortest edges is 1:$\sqrt{15}$/3 ≈ 1:1.29099.

Vertex coordinates
Coordinates for the vertices of a bidecachoron, based on two pentachora of edge length 1, centered at the origin, are given by:
 * (0, 0, 0, ±$\sqrt{10}$/5)
 * (0, 0, –$\sqrt{6}$/4, $\sqrt{10}$/20)
 * (0, 0, $\sqrt{6}$/4, –$\sqrt{10}$/20)
 * (0, –$\sqrt{3}$/3, $\sqrt{6}$/12, $\sqrt{10}$/20)
 * (0, $\sqrt{3}$/3, –$\sqrt{6}$/12, –$\sqrt{10}$/20)
 * (±1/2, $\sqrt{3}$/6, $\sqrt{6}$/12, $\sqrt{10}$/20)
 * (±1/2, –$\sqrt{3}$/6, –$\sqrt{6}$/12, –$\sqrt{10}$/20)

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Tetragonal disphenoid (30): Decachoron
 * Isosceles triangle (60): Rectified decachoron
 * Edge (20): Small prismatodecachoron
 * Edge (20): Biambodecachoron