Skewed muoctahedron
Skewed muoctahedron | |
---|---|
Rank | 3 |
Dimension | 3 |
Space | Euclidean |
Notation | |
Schläfli symbol | , |
Elements | |
Faces | N triangular helices |
Edges | N×2M |
Vertices | N×M |
Vertex figure | Square |
Petrie polygons | N triangular helices |
Holes | Apeirogons |
Related polytopes | |
Regiment | Skewed muoctahedron |
Petrie dual | Skewed muoctahedron |
Abstract & topological properties | |
Schläfli type | {∞,4} |
Properties | |
Chiral | Yes |
Convex | No |
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 (σ ) the muoctahedron, an operation abstractly equivalent to where π is the Petrie dual, δ is the dual, and η 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.
External links[edit | edit source]
- jan Misali (2020). "there are 48 regular polyhedra".
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.