Regular solids in all dimensions

   While we are all familiar with regular polygons (equilateral triangles, 
squares, ...), and many of us know about the Platonic, or regular solids 
(tetrahedron, cube, octahedron,....), few are familiar with their analogs 
in dimensions four and higher. Of course, this is because we are not 
equipped to perceive four-dimensional space directly.

    Nevertheless, the description of the regular solids in all dimensions 
has been known for a long time. The purpose of my talk will be to introduce 
you to these objects, with an emphasis on how to think about them. This 
presentation will be spiced up with some models of four-dimensional regular 
solids, some of which you can build yourself.