Here you can walk into a rectangular dodecahedron, a shape which is possible 
only in negatively curved hyperbolic 
space.  With a wand, you can summon and play with the of soap films in 
positively curved elliptic space.  You can see how to sew the edges of
hyperbolic octagons together into the surface of a 2-holed donut.  The CAVE
becomes a spaceship you can navigate with the wand, as it glides through
the phantasmic shapes that populate the 3-sphere.
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The purpose of this project is to perfect persuasive visual and sonic
environments in which to exhibit geometrical wonders and their startling
metamorphoses, which interest research geometers.  Convincing
visualizations of multi-dimensional, time-varying geometrical structures
are equally useful in applied and pure mathematics.
<p>