Hellenica World

Truncated tesseract

Truncated tesseract, Schlegel diagram
(tetrahedron cells visible)

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.


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 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.


Related uniform polytopes

Name tesseract rectified
tesseract
truncated
tesseract
cantellated
tesseract
runcinated
tesseract
bitruncated
tesseract
cantitruncated
tesseract
runcitruncated
tesseract
omnitruncated
tesseract
Coxeter-Dynkin
diagram
Schläfli
symbol
Schlegel
diagram
 
Name 16-cell rectified
16-cell
truncated
16-cell
cantellated
16-cell
runcinated
16-cell
bitruncated
16-cell
cantitruncated
16-cell
runcitruncated
16-cell
omnitruncated
16-cell
Coxeter-Dynkin
diagram
Schläfli
symbol
Schlegel
diagram

Images: Robert Webb's Great Stella software

Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License

Index

Scientific Library - Scientificlib.com