A semi - hypercube is a geometric body resulting from the alternation (removal of half of the vertices (alternating)) of a hypercube . In spaces with dimensions 3 and 4, half-hypercubes are the correct polytopes. In spaces of dimension 5 and above, semi-hypercubes are irregular but homogeneous polytopes, that is, their three-dimensional faces are regular polygons, although their hyper faces are not regular polytopes. Moreover, a five-dimensional semi-hypercube, called a semi- pentect , is a semi-regular polytope (this means that its hyper faces are different regular polytopes).
The name of the semi-hypercube is constructed as follows: the name of the original hypercube is added to the semi- prefix.
The vertex figure of a semi-hypercube is a fully truncated simplex of dimension n-1, where n is the dimension of the semi-hypercube itself. Special cases:
| The number of measurements n | Hypercube | Hypercube Image | Semi-hypercube | Image of a semi-hypercube |
|---|---|---|---|---|
| 2 | square |  | section |  |
| 3 | cube |  | regular tetrahedron |  |
| four | tesseract |  | sixteen cell |  |
| five | pentect |  | semi-act |  |
| 6 | hexeract |  | halfhexeract |  |
| 7 | heptect |  | semiheptect |  |
| eight | octact |  | semi-octect |  |
| 9 | enneract |  | half-energetic |  |
| ten | dekeract |  | half-act |  |
See also
Hypercube
Literature
- T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900