The stereoptic images below are 2 different rotations of a hypercube projected into 3-Space. These projections are orthogonal (there is no perspective). The edges shown in blue are the boundaries of the surfaces that enclose the 3-D form or "envelope".

To view these figures in stereo, you must look at them cross-eyed. The objective is to visually merge the 2 separate images into a single 3rd image which will appear between the original 2. It may help to focus your eyes on your index finger which should be held half way between your eyes and the screen. Once you see the 3 images (fuzzy beyond your finger) slowly concentrate on bringing them into focus without loosing the middle one. Remove your finger. If you have never done this before it will take some practice.

Rhombic Dodecahedron Envelope


This figure may be visualized as a rhombic dodecahedron with the opposite vertices, which are surrounded by three faces, connected. In this projection all 8 bounding cubes touch in the center of the 3-D figure. The rhombic dodecahedron is also one of the envelopes of the 24-cell.

Hexagonal Prism Envelope


This hexagonal prism, is a special case of the rhombic dodecahedral envelope where 2 of the bounding cube cells have been flattened out into hexagonal planes. This view is one of the most commonly published projections in 2-D. It is interesting that the hexagonal prism is also the edge first, midpoint cross-section of the hypercube.
Hyperspace
Last revised 10/20/02