  A data structure and toolkit are presented here that allow for the
description and manipulation of mathematical models of three-manifolds and
their interactive display from multiple viewpoints via the OpenGL 3D graphics
package. The data structure and vector math package can be extended to support
an arbitrary number of Euclidean spatial dimensions.
  A model in 4-space is described by its bounding pure simplicial 3-complex. By
intersecting a 3-flat with this 3-manifold, the algorithm will extract the
requested closed pure simplicial 2-complex surface enclosing the desired 3D
slice. The user can interactively rotate, pan, zoom, and shade arbitrary 3D
solid or wire-frame views of the revealed 3D object created by intersection,
thus exploring both expected and unexpected symmetries or asymmetries in the
world of 3-manifolds in 4-space.
