Tetrahelical triangular tiling

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Tetrahelical triangular tiling
Schläfli symbol[1]
Facestriangular helices
Vertex figureTriangle
Related polytopes
RegimentTrihelical square tiling
Petrie dualTrihelical square tiling
Abstract properties
Schläfli type{∞,3}

The tetrahelical triangular tiling or facetted halved mucube is a regular skew apeirohedron that consists of triangular helices, with three at a vertex. It is the Petrie dual of the trihelical square tiling. It is also the second-order facetting of the halved mucube[2], so the edges and vertices of the tetrahelical triangular tiling are a subset of those found in the halved mucube.

Vertex coordinates[edit | edit source]

The vertex coordinates of a tetrahelical triangular 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.