Halved mucube

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Halved mucube
Schläfli symbol,
Facesskew hexagons
Vertex figureHexagon
Petrie polygonsSkew squares
HolesTriangular helices
Related polytopes
DualHalved mucube
Petrie dualPetrial halved mucube
φ 2 Trihelical square tiling
Convex hullTetrahedral-octahedral honeycomb
Abstract & topological properties
Schläfli type{6,6}
Dimension vector(2,1,2)

The halved mucube is a regular skew apeirohedron within 3-dimensional space. It is an infinite polyhedron consisting of skew hexagons with 6 meeting at a vertex, and it can be obtained by halving or alternating the mucube. It has the Schläfli symbol {6,6}4 and it is self-dual.

Vertex coordinates[edit | edit source]

The vertex coordinates of the halved mucube of edge length 1 are the same as the vertex coordinates of the tetrahedral-octahedral honeycomb, being:

  • ,

where i , j  and k  are integers where i+j+k  is even.

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The halved mucube's Petrie polygon is a skew square, and its Petrial is the Petrial halved mucube.

One can apply a second-order facetting onto the halved mucube to obtain the tetrahelical triangular tiling.

Rectifying the halved mucube gives the muoctahedron.

External links[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.