Message #1422

From: Roice Nelson <>
Subject: Re: [MC4D] Regular Polytopes in 4D
Date: Wed, 16 Feb 2011 17:48:07 -0600

Yep, the 5-cell, 8-cell, and 120-cell are the only ones offered by MC4D
currently. These are the 4D regular polytopes having simplex vertex figures
(4 cells meeting at each vertex). That restriction simplifies the coding
situation (and puzzle difficulty for that matter).

I’m also not aware of any software which offers the others. Andrey has
talked about making 4D twisty puzzles without simplex vertex figures though,
and at the prodigious rate he’s been producing puzzles, I wouldn’t be
surprised to see one or more of the others realized in the not too distant

Despite their nonexistence, there has still been lively discussion here
lately about the nature of these puzzles. See this


On Wed, Feb 16, 2011 at 3:54 PM, Eduard <> wrote:

> There are only 6 regular polytopes in 4D.
> - The 5-cell corresponding to the tetrahedron in 3D
> - The 8-cell corresponding to the cube in 3D
> - The 16-cell corresponding to the octahedron in 3D
> - The 24-cell corresponding to nothing in 3D
> - The 120-cell corresponding to the dodecahedron in 3D
> - The 600-cell corresponding to the icosahedron in 3D
> Which of these are offered as sliced playable programs?
> I know 5-cell, 8-cell and 120-cell.