Stellated decachoron

{{Infobox polytope The Stellated decachoron is the simplest regular compound polychoron, and the third in the third in an infinite series of bi-simplex compounds. It is a compound of two pentachora in dual orientation.
 * type=Regular
 * dim = 4
 * obsa = Sted
 * cells = 10 tetrahedra
 * faces = 20 triangles
 * edges = 20
 * vertices = 10
 * verf = Tetrahedron, edge length 1
 * army=Bideca
 * reg=Sted
 * symmetry = A4⨯2, order 240
 * circum = $$\frac{2 \sqrt{10}}{5} ≈ 1.26491$$
 * inrad = $$\frac{\sqrt{10}}{10} ≈ 0.31623$$
 * hypervolume = $$\frac{\sqrt{5}}{48} ≈ 0.046585$$
 * dich= $$\arccos\left(\frac14\right) ≈ 75.52249°$$
 * dual=Stellated decachoron
 * conjugate=Stellated decachoron
 * orientable=Yes
 * nat=Tame