Rectified tesseract

The rectified tesseract, rit, rectified square duoprism, or digonal double prismantiprismoid, is a convex uniform polychoron that consists of 16 regular tetrahedra and 8 cuboctahedra. Two tetrahedra and three cuboctahedra join at each triangular prismatic vertex. As the name suggests, it can be obtained by rectifying the tesseract.

The rectified tesseract is the convex hull of two perpendicular digonal-square prismantiprismoids and is the first member of an infinite family of double prismantiprismoids and contains the vertices of two digonal-scalenohedral 8-3 double step prisms.

Vertex coordinates
The vertices of a rectified tesseract of edge length 1 are given by all permutations of:
 * (±$\sqrt{2}$/2, ±$\sqrt{6}$/2, ±$\sqrt{2}$/2, 0).

Alternatively, they can be given under D4 symmetry as even sign changes and all permutatoins of:


 * (3$\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4).

Representations
A rectified tesseract has the following Coxeter diagrams:


 * o4x3o3o (full symmetry)
 * x3o3x *b3o (D4 symmetry, as small rhombated demitesseract)
 * s4o3o3x (as runcic tesseract)
 * s4x3o3o (similar to above)
 * xxoo3oxxo3ooxx&#xt (A3 axial, tetrahedron-first)
 * oqo4xox3ooo&#xt (BC3 axial, cuboctahedron-first)
 * qo oq4xo3oo&#zx (BC3×A1 symmetry)
 * ox4qo xo4oq&#zx (BC2×BC2 symmetry, rectified square duoprism)
 * x(uo)x3o(oo)o3x(uo)x&#xt (A3 axial, cuboctahedron-first)
 * oxuxo xoxox4oqoqo&#xt (BC2×A1 axial, square-first)
 * oqoqoqo oooxuxo3oxuxooo&#xt (A2×A1 symmetry, vertex-first)

Related polychora
When viewed in A3 axial symmetry, the rectified tesseract can be seen as a central truncated tetrahedral cupoliprism with 2 tetrahedron atop truncated tetrahedron segmentochora attached to its bases.

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Cuboctahedron (8): Hexadecachoron
 * Tetrahedron (16): Tesseract
 * Square (24): Icositetrachoron
 * Triangle (64): Semi-uniform small disprismatotesseractihexadecachoron
 * Edge (96): Cantellated tesseract