Chaim Goodman-Strauss

This is an illustration of a symmetry of space, denoted (4_1*:2) in the Conway-Thurston notation (International Crystallographic No. 110), part of a suite of such images, created for the book, The Symmetries of Things, written with John H. Conway and Heidi Burgiel.

One of many similar pieces illustrating the four-dimensional point groups, this shows a group of order 48x8, which has as subgroups three perpendicular flows shown in the three colors. It, in turn, is a subgroup of the symmetries of the 24 cell, the 48 nodes here lying on the vertices of a pair of dual 24 cells. Its edges lie on those of a compound of two compounds of three 16-cells.