In the geometry of hyperbolic 3-space, the order-7 tetrahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,3,7}. It has seven tetrahedra {3,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many tetrahedra existing around each vertex in an order-7 triangular tiling vertex arrangement.
It is a part of a sequence of regular polychora and honeycombs with tetrahedral cells, {3,3,p}.
It is a part of a sequence of hyperbolic honeycombs with order-7 triangular tiling vertex figures, {p,3,7}.
It is a part of a sequence of hyperbolic honeycombs, {3,p,7}.
In the geometry of hyperbolic 3-space, the order-8 tetrahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,3,8}. It has eight tetrahedra {3,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many tetrahedra existing around each vertex in an order-8 triangular tiling vertex arrangement.
It has a second construction as a uniform honeycomb, Schläfli symbol {3,(3,4,3)}, Coxeter diagram, , with alternating types or colors of tetrahedral cells. In Coxeter notation the half symmetry is [3,3,8,1<sup>+</sup>] = [3,((3,4,3))].
In the geometry of hyperbolic 3-space, the infinite-order tetrahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,3,âÂÂ}. It has infinitely many tetrahedra {3,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many tetrahedra existing around each vertex in an infinite-order triangular tiling vertex arrangement.
It has a second construction as a uniform honeycomb, Schläfli symbol {3,(3,âÂÂ,3)}, Coxeter diagram, = , with alternating types or colors of tetrahedral cells. In Coxeter notation the half symmetry is [3,3,âÂÂ,1<sup>+</sup>] = [3,((3,âÂÂ,3))].