4-6 duoprism

Uniform 4-6 duoprisms 140px Schlegel diagrams
Type	Prismatic uniform polychoron
Schläfli symbol	{4}×{6}
Coxeter diagrams
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

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 cells exist in some of the uniform 5-polytopes in the B5 family.

Images

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4-6 duopyramid

4-6 duopyramid
Type	duopyramid
Schläfli symbol	{4}+{6}
Coxeter diagrams
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, facet-transitive

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

Orthogonal projection

Related polytopes

The 2-3 duoantiprism is an alternation of the 4-6 duoprism, represented by , but is not uniform. It has a highest symmetry construction of order 24, with 22 cells composed of 4 octahedra (as triangular antiprisms) and 18 tetrahedra (6 tetragonal disphenoids and 12 digonal disphenoids). There exists a construction with regular octahedra with an edge length ratio of 1 : 1.155. The vertex figure is an augmented triangular prism, which has a regular-faced variant that is not isogonal.

Vertex figure for the 2-3 duoantiprism

See also

• Polytope and polychoron
• Convex regular polychoron
• Duocylinder
• Tesseract

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