|Faces||N triangular helices|
|Petrie polygons||N triangular helices|
|Petrie dual||Skewed muoctahedron|
|Abstract & topological properties|
The skewed muoctahedron is a regular skew polyhedron within 3-dimensional space. It is an infinite polyhedron consisting of triangular helices, with 4 at a vertex. Like the hemidodecahedron, the skewed muoctahedron is self-Petrie; it is its own Petrie dual. Its vertices and edges are a subset of those found in the cubic honeycomb.
The skewed muoctahedron can be obtained by skewing () the muoctahedron, an operation abstractly equivalent to where is the Petrie dual, is the dual, and is halving. Despite the fact that some intermediate steps in the process of skewing cannot exist in 3D space, the final result ends up having a realization.
The skewed muoctahedron is a chiral polyhedron; its helices are either all clockwise or all counterclockwise.
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- jan Misali (2020). "there are 48 regular polyhedra".