6-8 duoprism
Type | Prismatic uniform polychoron |
Schläfli symbol | {6}×{8} {6}×t{4} t{3}×{8} t{3}×t{4} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 6 octagonal prisms, 8 hexagonal prisms |
Faces | 48 squares 6 octagons 8 hexagons |
Edges | 96 |
Vertices | 48 |
Vertex figure | Digonal disphenoid |
Symmetry | [6,2,8], order 96 |
Dual | 6-8 duopyramid |
Properties | convex, vertex-uniform |
In geometry of 4 dimensions, a 6-8 duoprism, a duoprism and 4-polytope resulting from the Cartesian product of a hexagon and an octagon.
Images
Image | ![]() |
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Center | Octagonal prism | Hexagonal prism |
6-8 duopyramid
6-8 duopyramid | |
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Type | duopyramid |
Schläfli symbol | {6}+{8} {6}+t{4} t{3}+{8} t{3}+t{4} |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 48 digonal disphenoids |
Faces | 96 isosceles triangles |
Edges | 62 (48+6+8) |
Vertices | 14 (6+8) |
Symmetry | [6,2,8], order 96 |
Dual | 6-8 duoprism |
Properties | convex, facet-transitive |
The dual of a 6-8 duoprism is called a 6-8 duopyramid. It has 48 digonal disphenoid cells, 96 isosceles triangular faces, 62 edges, and 14 vertices.
See also
Notes
References
- Regular Polytopes, H. S. M. Coxeter, Dover Publications, Inc., 1973, New York, p. 124.
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26)
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- N. W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
- Catalogue of Convex Polychora, section 6, George Olshevsky.
External links
- The Fourth Dimension Simply Explained—describes duoprisms as "double prisms" and duocylinders as "double cylinders"
- Polygloss – glossary of higher-dimensional terms
- Exploring Hyperspace with the Geometric Product
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