Related Polytopes and Tessellations
The, Coxeter group generates 31 permutations of uniform tessellations, 19 with unique symmetry and 18 with unique geometry. The expanded tesseractic honeycomb (also known as the stericated tesseractic honeycomb) is geometrically identical to the tesseractic honeycomb.
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The 24-cell honeycomb is similar, but as a body centered cubic, it has vertices positioned at integers (i,j,k,l), and half integers (i+1/2,j+1/2,k+1/2,l+1/2).
The tesseract can make a regular tessellation of the 4-sphere, with three tesseracts per face, with Schläfli symbol {4,3,3,3}, called a order-3 tesseractic honeycomb. It is topologically equivalent to the regular polytope penteract in 5-space.
The tesseract can make a regular tessellation of 4-dimensional hyperbolic space, with 5 tesseracts around each face, with Schläfli symbol {4,3,3,5}, called an order-5 tesseractic honeycomb.
Read more about this topic: Tesseractic Honeycomb
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