Truncated tesseract, Schlegel diagram
(tetrahedron cells visible)
In geometry, a truncated tesseract is a uniform polychoron (4dimensional uniform polytope) which is bounded by 24 cells: 8 truncated cubes, and 16 tetrahedra.
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.
The Cartesian coordinates of the vertices of a truncated tesseract having edge length 2 is given by all permutations of:
Projections
A stereoscopic 3D projection of a truncated tesseract.
In the truncated cube first parallel projection of the truncated tesseract into 3dimensional 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.
Related uniform polytopes
Name 
tesseract 
rectified
tesseract 
truncated
tesseract 
cantellated
tesseract 
runcinated
tesseract 
bitruncated
tesseract 
cantitruncated
tesseract 
runcitruncated
tesseract 
omnitruncated
tesseract 
CoxeterDynkin
diagram 

Schläfli
symbol 
Schlegel
diagram 

Name 
16cell 
rectified
16cell 
truncated
16cell 
cantellated
16cell 
runcinated
16cell 
bitruncated
16cell 
cantitruncated
16cell 
runcitruncated
16cell 
omnitruncated
16cell 
CoxeterDynkin
diagram 

Schläfli
symbol 
Schlegel
diagram 
Images: Robert Webb's Great Stella software