octahedron

I wouldn't really call the 24-cell "a strange version" of the octahedron.

Those meshes are made by subdividing an octahedron.

Sincere question, can someone explain how this[1] is an octahedron?

An octahedron looks like a square from three orthogonal directions, same as a cube.

Ex: The six surface midpoints of a cube are the six vertices of a regular octahedron; and vice versa.

I'm using Timeular which is an octahedron with erasable sides.

The octahedron defines the positions you pre-render the impostors from.

>someone could have a telephoto lens and take pictures of your dice rolls<Roll a braille octahedron in your bathroom with the door locked and the lights out. Type the bits on an offline computer so the keylogger can't report back to its owner.

Duckgoing for "octahedral sphere" brings up things like a tutorial on "creating better spheres by subdividing an octahedron".

'octahedral' could mean it has the same symmetries as an octahedron, not necessarily that it's an octahedron.

Basically it subdivides the sides of an octahedron to approximate a sphere.

When you mention tiling an octahedron with hexagons, the first thing I imagine is a truncated octahedron, which is composed of hexagons and squares.

The ideal cubic structure has the B cation in 6-fold coordination, surrounded by an octahedron of anions, and the A cation in 12-fold cuboctahedral coordination."[...

I am assuming that this is because that sphere-like object is generated by subdividing and inflating an octahedron, rather than the "sphere" primitive found in a lot of 3d programs.

By ordering the solids correctly—octahedron, icosahedron, dodecahedron, tetrahedron, and cube—Kepler found that the spheres correspond to the relative sizes of each planet's path around the Sun, generally varying from astronomical observations by less than 10%.