3-4 duoprism
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Uniform 3-4 duoprisms![]() ![]() Schlegel diagrams | |
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Type | Prismatic uniform polychoron |
Schläfli symbol | {3}×{4} |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 3 square prisms, 4 triangular prisms |
Faces | 3+12 squares, 4 triangles |
Edges | 24 |
Vertices | 12 |
Vertex figure | ![]() Digonal disphenoid |
Symmetry | [3,2,4], order 48 |
Dual | 3-4 duopyramid |
Properties | convex, vertex-uniform |
In geometry of 4 dimensions, a 3-4 duoprism, the second smallest p-q duoprism, is a 4-polytope resulting from the Cartesian product of a triangle and a square.
The 3-4 duoprism exists in some of the uniform 5-polytopes in the B5 family.
Images
![]() Net |
![]() 3D projection with 3 different rotations |
![]() Skew orthogonal projections with primary triangles and squares colored |
Related complex polygons
The quasiregular complex polytope 3{}×4{}, , in has a real representation as a 3-4 duoprism in 4-dimensional space. It has 12 vertices, and 4 3-edges and 3 4-edges. Its symmetry is 3[2]4, order 12.[1]
Related polytopes
The birectified 5-cube, has a uniform 3-4 duoprism vertex figure:
3-4 duopyramid
3-4 duopyramid | |
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Type | duopyramid |
Schläfli symbol | {3}+{4} |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 12 digonal disphenoids |
Faces | 24 isosceles triangles |
Edges | 19 (12+3+4) |
Vertices | 7 (3+4) |
Symmetry | [3,2,4], order 48 |
Dual | 3-4 duoprism |
Properties | convex, facet-transitive |
The dual of a 3-4 duoprism is called a 3-4 duopyramid. It has 12 digonal disphenoid cells, 24 isosceles triangular faces, 12 edges, and 7 vertices.
![]() Orthogonal projection |
![]() Vertex-centered perspective |
See also
Notes
- ^ Coxeter, H. S. M.; Regular Complex Polytopes, Cambridge University Press, (1974).
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
- 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