|Bowers style acronym||Ope|
|Coxeter diagram||x o4o3x ()|
|Cells||8 triangular prisms, 2 octahedra|
|Faces||16 triangles, 12 squares|
|Vertex figure||Square pyramid, edge lengths 1 (base), √2 (legs)|
|Measures (edge length 1)|
|Heights||Oct atop oct: 1|
|Trip atop gyro trip:|
|Number of pieces||10|
|Level of complexity||4|
|Symmetry||B3×A1, order 96|
The octahedral prism or ope is a prismatic uniform polychoron that consists of 2 octahedra and 8 triangular prisms. Each vertex joins 1 octahedron and 4 triangular prisms. It is a prism based on the octahedron. As such it is also a convex segmentochoron (designated K-4.11 on Richard Klitzing's list).
Gallery[edit | edit source]
Card with cell counts, verf, and cross-sections
Segmentochoron display, oct atop oct
Segmentochoron display, trip atop gyro trip
Vertex coordinates[edit | edit source]
Coordinates for the vertices of an octahedral prism of edge length 1 are given by all permutations of the first three coordinates of:
Representations[edit | edit source]
An octahedral prism has the following Coxeter diagrams:
- x o4o3x (full symmetry)
- x o3x3o () (base has A3 symmetry, tetratetrahedral prism)
- x2s2s3s () (triangular antiprismatic prism)
- x2s2s6o () (base has G2×A1+ symmetry)
- oo4oo3xx&#x (bases considered separately)
- oo3xx3oo&#x (bases considered in tet symmetry)
- xx xo3ox&#x (A2×A1 axial. trip atop gyro trip)
- xxx oxo4ooo&#xt (BC2×A1 symmetry, as square bipyramidal prism)
- xxx oxo oxo&#xt (A1×A1×A1 symmetry, as rectangular bipyramidal prism)
- xxx xox oqo&#xt (A1×A1×A1 axial, bases are edge-first)
- xxx qoo oqo ooq&#zx (A1×A1×A1×A1 symmetry, as rhombic bipyramidal prism)
- xx qo ox4oo&#zx (BC2×A1×A1 symmetry)
Related polychora[edit | edit source]
An octahedral prism can be cut into 2 square pyramidal prisms joining at a common cubic cell. If one half is rotated the result is instead a dyadic gyrotegmipucofastegium, which is also a segmentochoron.
The regiment of the octahedral prism also includes the tetrahemihexahedral prism.
External links[edit | edit source]
- Bowers, Jonathan. "Category 19: Prisms" (#890).
- Klitzing, Richard. "Ope".
- Wikipedia Contributors. "Octahedral prism".
- Hi.gher.Space Wiki Contributors. "Octahedral prism".