These two tetrahedra's vertices combined are the vertices of a cube, demonstrating that the regular tetrahedron is the 3-demicube.
12.
The regular tetrahedron is self-dual, which means that its compound figure comprising two such dual tetrahedra form a stellated octahedron or stella octangula.
13.
Suppose I am a budding mathematician and I have come to suspect that there is some kind of commonality between the cube and the regular tetrahedron.
14.
The Pyraminx is a puzzle in the shape of a regular tetrahedron, divided into 4 axial pieces, 6 edge pieces, and 4 trivial tips.
15.
The 4-simplex and pyramid-over-cube you're talking about are joins of a regular tetrahedron or cube with a single point.
16.
If you inscribe a regular tetrahedron in a sphere and then circumscribe another regular tetrahedron about the sphere, what's the ratio of their volumes?
17.
If you inscribe a regular tetrahedron in a sphere and then circumscribe another regular tetrahedron about the sphere, what's the ratio of their volumes?
18.
The closest and farthest cells are projected to inscribed tetrahedra within the cube, corresponding with the two possible ways to inscribe a regular tetrahedron in a cube.
19.
The vertices of a cube can be grouped into two groups of four, each forming a regular tetrahedron; more generally this is referred to as a demicube.
20.
You can see the tetrahedral slices of the hypercube similarly-the red vertices can be joined together to make a regular tetrahedron, and the purple vertices likewise.
