The early history of research in electromagnetism and optics is wonderful. It’s amazing, for example, how much people learned about electric current back when the only way of measuring its strength was feeling how strong the electrical shock you got from it.

]]>I might re-read Whittaker’s tome to see what dimension it transports me to!!

Cheers

Peter ]]>

Hmm, this seems to be studied in somewhat different language here:

• Steve Fisk, Coloring the 600-cell.

Abstract.The 600 cell S has exactly 10 5-colorings. From these colorings we can construct the space of colorings B(S). This complex has 1344 colorings, and is isomorphic to the space of 5 by 5 Latin squares. These simplices split into 4 copies of a quotient of S by an involution, and two copies of a space made up of even Latin squares.

His space B(S) has 25 vertices which seem to be the 25 24-cells inscribed in a 600-cell.

]]>Someday people will have a lot of fun with such games.

]]>Cool! I’ve added a link to your paper.

]]>Reminds me of a project to use the vertices and edges of various uniform polychora as Go boards.

]]>I always thought that space-exploration games with bounded flat two-dimensional universe were kind of stupid.

— hendrik

]]>The trick is that the vertices of the 600-cell form a group: the ‘binary icosahedral group’, called There’s a way to inscribe a 24-cell in it so that its vertices form a subgroup called the ‘binary tetrahedral group’, Then we can choose an element of order 5 such that the 25 different 24-cells are of the form

where So that gives us a 5 × 5 array of them!

]]>