User:Tetracube/Gallery of polychora

Welcome to the gallery of polychoron images!

This page is intended to collect images and animations of polychora to facilitate selecting the best ones for inclusion in the actual polychoron articles. The images will include vertex/edge/ridge/cell-first projections, with both perspective and parallel projections where the distinction matters, and possibly different combinations of enhancements applied to make the structure of the projection clearer.

Regular polychora
These are perspective projections of the regular polychora, scaled to an outradius of 1, and viewed 5 units away in 4-space. Note that all surfaces hidden from the 4D viewpoint (the facets on the far side of the polychoron) have been culled, for clarity.

The following enhancements have been applied to these images:
 * In vertex-first projections, the closest vertex is rendered as a small sphere in order to show its position within the projection image;
 * In edge-first projections, the closest edge is rendered as a thin cylinder;
 * In face-first projections, the closest face is highlighted;
 * In cell-first projections, the closest cell is highlighted, except where it fills up the entirety of the image.

Further enhanced images
Below are some further-enhanced images, to accentuate parts of the structure of the projections:

Uniform polychora
Uniform polychora images are grouped based on the positions of the elements of their base polychoron (taken to be the closest regular polychoron from which they are derived). For example, the base polychoron of the truncated 16-cell is the 16-cell, and the projection centered on a truncated tetrahedral cell is grouped under "base cell", and the projection centered on an octahedral cell is grouped under "base vertex". For the 5-cell and 24-cell groups, two of these elements are redundant because the base polychoron is self-dual.

Rotatopes
Various curved 4D objects.