Triangular-cubic duoprism

The triangular-cubic duoprism or tracube, also known as a triangular-square duoprismatic prism, is a convex uniform duoprism that consists of 3 tesseracts and 6 triangular-square duoprisms. Each vertex joins 2 tesseracts and 3 triangular-square duoprisms. It is a duoprism based on a triangle and a cube, which makes it a convex segmentoteron, and it can also be viewed as a duoprism based on a square and a triangular prism.

Vertex coordinates
The vertices of a triangular-cubic duoprism of edge length 1 are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac12,\,±\frac12\right).$$

Representations
A triangular-cubic duoprism has the following Coxeter diagrams:
 * x3o x4o3o (full symmetry)
 * x x3o x4o (triangular-square duoprismatic prism)
 * x x x x3o (triangular prismatic prismatic prism)
 * xx3oo xx4oo&#x (triangular-square duoprism atop triangular-square duoprism)
 * xx3oo xx xx&#x
 * ox xx xx4oo&#x (cube atop tesseract)
 * ox xx xx xx&#x
 * xxx xxx xxx&#x