Truncated tesseract  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. The truncated tesseract may be constructed by truncating the vertices of the tesseract at formula_1 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 "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. 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. The Cartesian coordinates of the vertices of a bitruncated tesseract having edge length 2 is given by all permutations of:  The truncated octahedra are connected to each other via their square faces, and to the truncated tetrahedra via their hexagonal faces. The truncated tetrahedra are connected to each other via their triangular faces. The truncated-octahedron-first projection of the bitruncated tesseract into 3D space has a truncated cubical envelope. Two of the truncated octahedral cells project onto a truncated octahedron inscribed in this envelope, with the square faces touching the centers of the octahedral faces.