Balls and Straws
Ghost Symmetry


This project started with a desire to make physical models of ghost symmetry. This page illustrates two of these models.

The 24-Cell, with Dodecagonal Ghost Symmetry.

Ideally, this model has two shadows each having 12-fold dihedral symmetry. This occurs despite the fact that the symmetry group of the 3-dimensional model does not contain this group. In fact, the symmetry group of the physical model is merely a direct product of three copies of the 2-element group C2. The action is generated by the reflections across the three coordinate planes. In other words, each coordinate plane acts like a mirror:

DR with Ghastly 24-Cell

The A(4) Root System.

This model was derived from the projection of the 5-cell having 5-fold ghost symmetry. While this 3-dimensional object has no 10-fold symmetry, it has two different shadows which have 10-fold dihedral symmetry. One can see this symmetry on Vorthmann's page.

The A(4) Root System, with Decagonal Ghost Symmetry.

Index to Balls and Straws
Index to Polyhedra