Hemitesseract should not be confused with Demitesseract.
| Hemitesseract (hemi-4-cube) | |
| Type: | Regular projective 4-polytope |
| Schläfli: | /2 or 4 |
| Face List: | 12 |
| Edge Count: | 16 |
| Vertex Count: | 8 |
| Petrie Polygon: | Square |
| Vertex Figure: | Tetrahedron |
| Dual: | hemi-16-cell |
In abstract geometry, a hemitesseract is an abstract, regular polyhedron, containing half the cells of a tesseract, existing in real projective space, RP3.
It has four cubic cells, 12 square faces, 16 edges, and 8 vertices. It has an unexpected property that every cell is in contact with every other cell on two faces, and every cell contains all the vertices, which gives an example of an abstract polytope whose faces are not determined by their vertex sets.
From the point of view of graph theory, the skeleton is a cubic graph with 8 diagonal central edges added.
It is also the complete bipartite graph K4,4, and the regular complex polygon 24, a generalized cross polytope.
This configuration matrix represents the hemitesseract. The rows and columns correspond to vertices, edges, faces, and cells. The diagonal numbers say how many of each element occur in the whole hemitesseract. The nondiagonal numbers say how many of the column's element occur in or at the row's element.[1] For example, the 2 in the first column of the second row indicates that there are 2 vertices in (i.e., at the extremes of) each edge; the 4 in the second column of the first row indicates that 4 edges meet at each vertex.
\begin{bmatrix}\begin{matrix}8&4&6&4\ 2&16&3&3\ 4&4&12&2\ 8&12&6&4\end{matrix}\end{bmatrix}