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The cell-first parallel projection of the tesseract into three-dimensional space has a cubical envelope. The nearest and farthest cells are projected onto the cube, and the remaining six cells are projected onto the six square faces of the cube. The face-first parallel projection of the tesseract into three-dimensional space has a cuboidal ...
This layout of cells in projection is analogous to the layout of faces in the projection of the truncated cube into 2 dimensions. Hence, the cantellated tesseract may be thought of as an analogue of the truncated cube in 4 dimensions. (It is not the only possible analogue; another close candidate is the truncated tesseract.)
The cube's vertex-first projection has three tetragons surrounding a vertex, but the tesseract's vertex-first projection has four hexahedral volumes surrounding a vertex. Just as the nearest corner of the cube is the one lying at the center of the image, so the nearest vertex of the tesseract lies not on the boundary of the projected volume ...
In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract.It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.
In geometry, a Schlegel diagram is a projection of a polytope from into through a point just outside one of its facets. The resulting entity is a polytopal subdivision of the facet in R d − 1 {\textstyle \mathbb {R} ^{d-1}} that, together with the original facet, is combinatorially equivalent to the original polytope.
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.
It is a part of an infinite hypercube family. The dual of a 5-cube is the 5-orthoplex, of the infinite family of orthoplexes.. Applying an alternation operation, deleting alternating vertices of the 5-cube, creates another uniform 5-polytope, called a 5-demicube, which is also part of an infinite family called the demihypercubes.
In the cuboctahedron-first parallel projection of the rectified tesseract into 3-dimensional space, the image has the following layout: The projection envelope is a cube . A cuboctahedron is inscribed in this cube, with its vertices lying at the midpoint of the cube's edges.