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The dissection of the tesseract into instances of its characteristic simplex (a particular orthoscheme with Coxeter diagram ) is the most basic direct construction of the tesseract possible. The characteristic 5-cell of the 4-cube is a fundamental region of the tesseract's defining symmetry group , the group which generates the B 4 polytopes .
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Tesseract central projection from vertex 0000 gives a 3-dimensional shadow, with a tetrahedral convex hull. The four bits are arranged like the vertices of this Hasse diagram: Date: 2010: Source: Own work: Author
English: The Gray code in its Wikipedia article as a traversal of vertices of a tesseract by CMG Lee. Note: The LSB axis is vertical (instead of the usual horizontal x-axis) to reduce the number of path self-crossings while starting near the top left.
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The full snub tesseract or omnisnub tesseract, defined as an alternation of the omnitruncated tesseract, can not be made uniform, but it can be given Coxeter diagram , and symmetry [4,3,3] +, and constructed from 8 snub cubes, 16 icosahedra, 24 square antiprisms, 32 octahedra (as triangular antiprisms), and 192 tetrahedra filling the gaps at ...