Truncated tesseract
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| Truncated tesseract | |
|---|---|
 Schlegel diagram (tetrahedron cells visible) |
|
| Type | Uniform polychoron |
| Cells | 8 3.8.8  16 3.3.3  |
| Faces | 64 {3} 24 {8} |
| Edges | 128 |
| Vertices | 64 |
| Schläfli symbol | t0,1{4,3,3} |
| Coxeter-Dynkin diagrams |     |
| Symmetry group | A4, [4,3,3] |
| Properties | convex |
Vertex figure Three truncated cubes and one tetrahedron meet at each vertex in an equilateral-triangular pyramid arrangement. |
|
In geometry, a truncated tesseract is a uniform polychoron (4-dimensional uniform polytope) which is bounded by 24 cells: 8 truncated cubes, and 16 tetrahedra.
Contents |
[edit] Construction
The truncated tesseract may be constructed by truncating the vertices of the tesseract at 
of the edge length. A regular tetrahedron is formed at each truncated vertex.
[edit] Projections
In the truncated cube first parallel projection of the truncated tesseract into 3-dimensional space, the image is laid out as follows:
- The projection envelope is a cube.
- Two of the truncated cube cells project onto a truncated cube inscribed in the cubical envelope.
- The other 6 truncated cubes project onto the square faces of the envelope.
- The 8 tetrahedral volumes between the envelope and the triangular faces of the central truncated cube are the images of the 16 tetrahedra, a pair of cells to each image.
[edit] Images
 A polyhedral net |
.png/200px-Truncated_tesseract_stereographic_(tC).png) Truncated tesseract projected onto the 3-sphere with a stereographic projection into 3-space. |
