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Concept
Truncated tesseract
Summary
In geometry, a truncated tesseract is a uniform 4-polytope formed as the truncation of the regular tesseract.
There are three truncations, including a bitruncation, and a tritruncation, which creates the truncated 16-cell.
The truncated tesseract is bounded by 24 cells: 8 truncated cubes, and 16 tetrahedra.
Truncated tesseract (Norman W. Johnson)
Truncated tesseract (Acronym tat) (George Olshevsky, and Jonathan Bowers)
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:
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.
The truncated tesseract, is third in a sequence of truncated hypercubes:
The bitruncated tesseract, bitruncated 16-cell, or tesseractihexadecachoron is constructed by a bitruncation operation applied to the tesseract. It can also be called a runcicantic tesseract with half the vertices of a runcicantellated tesseract with a construction.
Bitruncated tesseract/Runcicantic tesseract (Norman W. Johnson)
Tesseractihexadecachoron (Acronym tah) (George Olshevsky, and Jonathan Bowers)
A tesseract is bitruncated by truncating its cells beyond their midpoints, turning the eight cubes into eight truncated octahedra. These still share their square faces, but the hexagonal faces form truncated tetrahedra which share their triangular faces with each other.
Official source
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