6-6 duoprism
Uniform 6-6 duoprism Schlegel diagram | |
---|---|
Type | Uniform duoprism |
Schläfli symbol | {6}×{6} = {6}2 |
Coxeter diagrams | |
Cells | 12 hexagonal prisms |
Faces | 36 squares, 12 hexagons |
Edges | 72 |
Vertices | 36 |
Vertex figure | Tetragonal disphenoid |
Symmetry | [[6,2,6]] = [12,2+,12], order 288 |
Dual | 6-6 duopyramid |
Properties | convex, vertex-uniform, facet-transitive |
In geometry of 4 dimensions, a 6-6 duoprism is a polygonal duoprism, a 4-polytope resulting from the Cartesian product of two octagons.
It has 36 vertices, 72 edges, 48 faces (36 squares, and 12 hexagons), in 12 hexagonal prism cells. It has Coxeter diagram , and symmetry [[6,2,6]], order 288.
Images
Net
Seen in a skew 2D orthogonal projection, it contains the projected rhombi of the rhombic tiling.
6-6 duoprism | Rhombic tiling |
---|---|
6-6 duoprism | 6-6 duoprism |
6-6 duopyramid
6-6 duopyramid | |
---|---|
Type | Uniform dual duopyramid |
Schläfli symbol | {6}+{6} = 2{6} |
Coxeter diagrams | |
Cells | 36 tetragonal disphenoids |
Faces | 72 isosceles triangles |
Edges | 48 (36+12) |
Vertices | 12 (6+6) |
Symmetry | [[6,2,6]] = [12,2+,12], order 288 |
Dual | 6-6 duoprism |
Properties | convex, vertex-uniform, facet-transitive |
The dual of a 6-6 duoprism is called a 6-6 duopyramid. It has 36 tetragonal disphenoid cells, 72 triangular faces, 48 edges, and 12 vertices.
It can be seen in orthogonal projection:
Skew | [6] | [12] |
---|
See also
- 3-3 duoprism
- 3-4 duoprism
- 5-5 duoprism
- Tesseract (4-4 duoprism)
- Convex regular 4-polytope
- Duocylinder
Notes
References
- Regular Polytopes, H. S. M. Coxeter, Dover Publications, Inc., 1973, New York, p. 124.
- Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999, ISBN 0-486-40919-8 (Chapter 5: Regular Skew Polyhedra in three and four dimensions and their topological analogues)
- Coxeter, H. S. M. Regular Skew Polyhedra in Three and Four Dimensions. Proc. London Math. Soc. 43, 33-62, 1937.
- 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
- Olshevsky, George, Duoprism at Glossary for Hyperspace.
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
This article is issued from Wikipedia - version of the Monday, April 04, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.