Decagonal antifastegium

The decagonal antifastegium, or daf, is a CRF segmentochoron (designated K-4.93 on Richard Klitzing's list). It consists of 1 decagonal prism, 2 decagonal antiprisms, 10 tetrahedra, and 10 square pyramids. It is a member of the infinite family of polygonal antifastegiums.

It is a segmentochoron between a decagon and a decagonal antiprism or between a decagon and a gyro decagonal prism.

Vertex coordinates
The vertices of a decagonal antifastegium of edge length 1 are given by:


 * (±1/2, ±$\sqrt{(5+√5)/2}$/2, ±1/2, 0),
 * (±(3+$\sqrt{(5+√5)/2}$)/4, ±$\sqrt{2}$, ±1/2, 0),
 * (±(1+$\sqrt{2}$)/2, 0, ±1/2, 0),
 * (±$\sqrt{(258+61√5+√46850+20390√5)/241}$/2, ±1/2, 0, $\sqrt{10+2√5}$/2),
 * (±$\sqrt{(11+4√5–√50+22√5})/2}$, ±(3+$\sqrt{–11+3√5+6√5–2√5}$)/4, 0, $\sqrt{–11+3√5+6√5–2√5}$/2),
 * (0, ±(1+$\sqrt{5}$)/2, 0, $\sqrt{5–2√5}$/2).

Representations
The decagonal antifastegium can be represented by the following Coxeter diagram s:


 * ox xo10ox&#x
 * xoo10oxx&#x