The stereoptic images below, are a Simplex 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 (Envelope).  See the Hypercube envelope page for instructions on how to view these figures.

Tetrahedron Envelope

Tetrahedron Envelope

This envelope is a tetrahedron. You may visualize this figure as a tetrahedron with it's vertices connected to it's center.  There are 4 bounding tetrahedral cells associated with of the envelopes faces and the 5th cell is the envelope itself.

Tetrahedron Envelope


If you have Red/Blue 3-D Comic Book classes, the image above may be easier to view.

Triangular Dipyramid Envelope


This view is probably the most common 2-D projection of the Simplex. The 3-space envelope is a dipyramid with a triangle as a base.  The 3 vertices defining the base of the dipyramid are surrounded by 4 triangles each and the remaining 2 by 3 triangles each.

Triangular Dipyramid Envelope
Hyperspace
Last Revision: 10/23/2002