| bgcolor=#e7dcc3 colspan=2 | 5-cube 5-orthoplex compound | |
|---|---|---|
| Type | Compound | |
| Schläfli symbol | ∪ | |
| Coxeter diagram | ∪ | |
| Intersection | Birectified 5-cube | |
| Convex hull | dual of rectified 5-orthoplex | |
| 5-polytopes | 2: 1 5-cube 1 5-orthoplex | |
| Polychora | 42: 10 tesseract 32 16-cell | |
| Polyhedra | 120: 40 cubes 80 tetrahedra | |
| Faces | 160: 80 squares 80 triangles | |
| Edges | 120 (80+40) | |
| Vertices | 42 (32+10) | |
| Symmetry group | B5, [4,3,3,3], order 3840 |
In 5-polytope compounds constructed as dual pairs, the hypercells and vertices swap positions and cells and edges swap positions. Because of this the number of hypercells and vertices are equal, as are cells and edges. Mid-edges of the 5-cube cross mid-cell in the 16-cell, and vice versa.
It can be seen as the 5-dimensional analogue of a compound of cube and octahedron.
The 42 Cartesian coordinates of the vertices of the compound are.
10: (±2, 0, 0, 0, 0), (0, ±2, 0, 0, 0), (0, 0, ±2, 0, 0), (0, 0, 0, ±2, 0), (0, 0, 0, 0, ±2)
32: (±1, ±1, ±1, ±1, ±1)
The convex hull of the vertices makes the dual of rectified 5-orthoplex.
The intersection of the 5-cube and 5-orthoplex compound is the uniform birectified 5-cube: = ∩ .
The compound can be seen in projection as the union of the two polytope graphs. The convex hull as the dual of the rectified 5-orthoplex will have the same vertices, but different edges.