Trihelical square tiling

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Trihelical square tiling
Schläfli symbol[1]
FacesN square helices
Vertex figureTriangle
Related polytopes
RegimentTrihelical square tiling
Petrie dualTetrahelical triangular tiling
Abstract properties
Schläfli type{∞,3}

The trihelical square tiling or petrial facetted halved mucube is a regular skew apeirohedron that consists of square helices, with three meeting at each vertex. All adjacent square helices in the trihelical square tiling that share a vertex are perpendicular to each other.

The trihelical square tiling is the Petrie dual of the tetrahelical triangular tiling. It also is the second-order facetting of the petrial halved mucube[2], so the edges and vertices of the trihelical square tiling are a subset of those found in the halved mucube.

Vertex coordinates[edit | edit source]

The vertex coordinates of a trihelical square tiling of edge length 1 are given by all permutations of:

where range over the integers.

External links[edit | edit source]

References[edit | edit source]

Bibliography[edit | edit source]

  • McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF). Discrete Computational Geometry (47): 449–478. doi:10.1007/PL00009304.