The stereoptic images below are 3 different rotations of a 16-Cell projected into 3-Space.  The edges shown in color are the boundaries of the surfaces that enclose the 3-D form or "envelope".

For instructions on how to view these images stereoptically, see the hypercube envelope page.  If you have Red/Blue 3-D comic book glasses, use them to view the alternate images.

Octahedron Envelope

Octahedron Envelope

In this 3-D projection, the 16 tetrahedral cells that bound this 4-D figure are mostly superimposed on each other.  Here you will see only 4 tetrahedra surrounding the gray line which joins 2 vertices of the octahedra.  Alternate Red/Blue images.

Cube Envelope

Cube Envelope

The 16 tetrahedra are somewhat more visible in this projection.  There are 2 fully formed tetrahedra are inscribed within the cube.  Each of the 6 faces of the cube contains another tetrahedra flattened out in a square plane.  Alternate Red/Blue images.

Hexagonal Dipyramid

Hexagonal Dipyramid

The 3-D envelope of this projection, is an irregular dipyramid whose base is a hexagon.  It is interesting because the same 4-D rotation produces the popular 2-D projection of the 16-Cell in which all 16 tetrahedral bounding cells are clearly visible.  There are 2 tetrahedra joining at each edge.  There appears to be an octahedron flattened to a hexagonal plane in the center (the base of the dipyramid).  This octahedron and the 5 others you may see here are not cells in the 4-D figures.  They are analogous to the 3 squares you will see in a wire model of an octahedron.  This envelope is the dual of the hexagonal prism envelope of the hypercube. Alternate Red/Blue images.
Hyperspace
Last revised 11/16/96