| 释义 |
- Images
- 4-8 duopyramid
- See also
- Notes
- References
- External links
Uniform 4-8 duoprisms
Schlegel diagrams | | Type | Prismatic uniform polychoron | | Schläfli symbols | {4}×{8}
{4}×t{4} | | Coxeter diagrams | node_1|4|node|2|node_1|8|node}}
{{CDD|node_1|4|node|2|node_1|4|node_1}}
{{CDD|node_1|2|node_1|2|node_1|8|node}}
{{CDD|node_1|2|node_1|2|node_1|4|node_1}} | | Cells | 4 octagonal prisms,
8 cubes | | Faces | 32+8 squares,
4 octagons | | Edges | 64 | | Vertices | 32 | | Vertex figure | Digonal disphenoid | | Symmetry | [4,2,8], order 64 | | Dual | 4-8 duopyramid | | Properties | convex, vertex-uniform |
In geometry of 4 dimensions, a 4-8 duoprism, a duoprism and 4-polytope resulting from the Cartesian product of a square and an octagon. It has 12 cells (4 octagonal prisms and 8 cubes), 44 faces (40 squares and 4 octagons), 64 edges, and 32 vertices. Images{{-}} 4-8 duopyramid | dual uniform 4-8 duopyramid | | Type | duopyramid | | Schläfli symbol | {4}+{8}
{4}+t{4} | | Coxeter-Dynkin diagram | node_f1|4|node|2x|node_f1|8|node}}
{{CDD|node_f1|4|node|2x|node_f1|4|node_f1}}
{{CDD|node_f1|2x|node_f1|2x|node_f1|8|node}}
{{CDD|node_f1|2x|node_f1|2x|node_f1|4|node_f1}} | | Cells | 32 digonal disphenoids | | Faces | 64 isosceles triangles | | Edges | 44 (32+4+8) | | Vertices | 12 (4+8) | | Symmetry | [4,2,8], order 64 | | Dual | 4-8 duoprism | | Properties | convex, facet-transitive |
The dual of a 4-8 duoprism is called a 4-8 duopyramid. It has 32 tetragonal disphenoid cells, 64 isosceles triangular faces, 44 edges, and 12 vertices. See also- Polytope and polychoron
- Convex regular polychoron
- Duocylinder
- Tesseract
NotesReferences- 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
- {{PolyCell | urlname =section6.html| title = Catalogue of Convex Polychora, section 6}}
External links- [https://web.archive.org/web/20030121092141/http://etext.lib.virginia.edu/etcbin/toccer-new2?id=ManFour.sgm&images=images%2Fmodeng&data=%2Ftexts%2Fenglish%2Fmodeng%2Fparsed&tag=public&part=all The Fourth Dimension Simply Explained]—describes duoprisms as "double prisms" and duocylinders as "double cylinders"
- [https://www.webcitation.org/query?url=http://www.geocities.com/os2fan2/gloss.htm&date=2009-10-26+00:04:35 Polygloss] – glossary of higher-dimensional terms
- [https://web.archive.org/web/20141201023452/http://www.bayarea.net/~kins/thomas_briggs/ Exploring Hyperspace with the Geometric Product]
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