onto the square faces of the cube. In this projection of the 16-cell, all its edges lie on the faces of the cubical envelope. The cell-first perspective projection of the 16-cell into 3-space has a triakis tetrahedral envelope. The layout of the cells within this envelope are analogous to that of the cell-first parallel projection. The vertex-first parallel projection of the 16-cell into 3-space has an octahedral envelope. This octahedron can be divided into 8 tetrahedral volumes, by cutting along the coordinate planes. Each of these volumes is the image of a pair of cells in the 16-cell. The closest vertex of the 16-cell to the viewer projects onto the center of the octahedron. Finally the edge-first parallel projection has a shortened octahedral envelope, and the face-first parallel projection has a hexagonal bipyramidal envelope. 4 sphere Venn diagram A 3-dimensional projection of the 16-cell and 4 intersecting spheres (a Venn diagram of 4 sets) are topologically equivalent. Symmetry constructions The 16-cell's symmetry group is denoted B4. There is a lower symmetry form of the 16-cell, called a demitesseract or 4-demicube, a member of the demihypercube family, and represented by h{4,3,3}, and Coxeter diagrams or . It can be drawn bicolored with alternating tetrahedral cells. It can also be seen in lower symmetry form as a tetrahedral antiprism, constructed by 2 parallel tetrahedra in dual configurations, connected by 8 (possibly elongated) tetrahedra. It is represented by s{2,4,3}, and Coxeter diagram: . It can also be seen as a snub 4-orthotope, represented by s{21,1,1}, and Coxeter diagram: or . With the tesseract constructed as a 4-4 duoprism, the 16-cell can be seen as its dual, a 4-4 duopyramid. Related complex polygons The Möbius–Kantor polygon is a regular complex polygon 3{3}3, , in shares the same vertices as the 16-cell. It has 8 vertices, and 8 3-edges. The regular complex polygon, 2{4}4, , in has a real representation as a 16-cell in 4-dimensional space with 8 vertices, 16 2-edges, only half of the edges of the 16-cell. Its symmetry is 4[4]2, order 32. Related uniform polytopes and honeycombs The regular 16-cell and tesseract are the regular members of a set of 15 uniform 4-polytopes with the same B4 symmetry. The 16-cell is also one of the uniform polytopes of D4 symmetry. The 16-cell is also related to the cubic honeycomb, order-4 dodecahedral honeycomb, and order-4 hexagonal tiling honeycomb which all have octahedral vertex