parallel projection of the tesseract into three-dimensional space has a rhombic dodecahedral envelope. Two vertices of the tesseract are projected to the origin. There are exactly two ways of dissecting a rhombic dodecahedron into four congruent rhombohedra, giving a total of eight possible rhombohedra, each a projected cube of the tesseract. This projection is also the one with maximal volume. One set of projection vectors are u=(1,1,-1,-1), v=(-1,1,-1,1), w=(1,-1,-1,1). Tessellation The tesseract, like all hypercubes, tessellates Euclidean space. The self-dual tesseractic honeycomb consisting of 4 tesseracts around each face has Schläfli symbol {4,3,3,4}. Hence, the tesseract has a dihedral angle of 90°. The tesseract's radial equilateral symmetry makes its tessellation the unique regular body-centered cubic lattice of equal-sized spheres, in any number of dimensions. Related polytopes and honeycombs The tesseract is 4th in a series of hypercube: The tesseract (8-cell) is the third in the sequence of 6 convex regular 4-polytopes (in order of size and complexity). As a uniform duoprism, the tesseract exists in a sequence of uniform duoprisms: {p}×{4}. The regular tesseract, along with the 16-cell, exists in a set of 15 uniform 4-polytopes with the same symmetry. The tesseract {4,3,3} exists in a sequence of regular 4-polytopes and honeycombs, {p,3,3} with tetrahedral vertex figures, {3,3}. The tesseract is also in a sequence of regular 4-polytope and honeycombs, {4,3,p} with cubic cells. The regular complex polytope 4{4}2, , in has a real representation as a tesseract or 4-4 duoprism in 4-dimensional space. 4{4}2 has 16 vertices, and 8 4-edges. Its symmetry is 4[4]2, order 32. It also has a lower symmetry construction, , or 4{}×4{}, with symmetry 4[2]4, order 16. This is the symmetry if the red and blue 4-edges are considered distinct. In popular culture Since their discovery, four-dimensional hypercubes have been a popular theme in art, architecture, and science fiction. Notable examples include: "And He Built a Crooked House", Robert Heinlein's 1940 science fiction story featuring a building in the form of a four-dimensional hypercube. This and Martin Gardner's "The No-Sided Professor", published in 1946, are among the first in science fiction to introduce readers to the Moebius band, the Klein bottle, and the hypercube (tesseract). Crucifixion (Corpus Hypercubus), a 1954 oil painting by Salvador Dalí featuring a four-dimensional hypercube unfolded into a three-dimensional Latin cross. The Grande Arche, a monument and building near Paris, France, completed in 1989. According to the monument's engineer, Erik Reitzel,