4-6 duoprism

Uniform 4-6 duoprisms Schlegel diagrams
Type	Prismatic uniform polychoron
Schläfli symbol	{4}×{6}
Coxeter–Dynkin diagram
Cells	4 hexagonal prisms, 6 square prisms
Faces	24+6 squares, 4 hexagons
Edges	48
Vertices	24
Vertex figure	Digonal disphenoid
Symmetry	[4,2,6], order 48
Dual	4-6 duopyramid
Properties	convex, vertex-uniform, facet-transitive

In geometry of 4 dimensions, a 4-6 duoprism, a duoprism and 4-polytope resulting from the Cartesian product of a square and a hexagon.

The 4-6 duoprism exists in some of the uniform 5-polytopes in the B5 family.

Images

Net

4-6 duopyramid

dual uniform 4-6 duopyramid
Type	duopyramid
Schläfli symbol	{4}+{6}
Coxeter-Dynkin diagram
Cells	24 digonal disphenoids
Faces	48 isosceles triangles
Edges	34 (24+4+6)
Vertices	10 (4+6)
Symmetry	[4,2,6], order 48
Dual	4-6 duoprism
Properties	convex, vertex-uniform, facet-transitive

The dual of a 4-6 duoprism is called a 4-6 duopyramid. It has 18 tetragonal disphenoid cells, 34 isosceles triangular faces, 34 edges, and 10 vertices.

Orthogonal projection

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.
- Catalogue of Convex Polychora, section 6, George Olshevsky.

External links