3-6 duoprism

Uniform 3-6 duoprisms Schlegel diagrams
Type	Prismatic uniform polychoron
Schläfli symbol	{3}×{6}
Coxeter–Dynkin diagram
Cells	3 hexagonal prisms, 6 triangular prisms
Faces	12 squares, 3 hexagons, 6 triangles
Edges	36
Vertices	18
Vertex figure	Digonal disphenoid
Symmetry	[3,2,6], order 36
Dual	3-6 duopyramid
Properties	convex, vertex-uniform

In geometry of 4 dimensions, a 3-6 duoprism, a duoprism and 4-polytope resulting from the Cartesian product of a triangle and a hexagon.

Images

Net

3-6 duopyramid

dual uniform 3-6 duopyramid
Type	duopyramid
Schläfli symbol	{3}+{6}
Coxeter-Dynkin diagram
Cells	18 digonal disphenoids
Faces	36 isosceles triangles
Edges	27 (18+3+6)
Vertices	9 (3+6)
Symmetry	[3,2,6], order 36
Dual	3-6 duoprism
Properties	convex, facet-transitive

The dual of a 3-6 duoprism is called a 3-6 duopyramid. It has 18 tetragonal disphenoid cells, 36 isosceles triangular faces, 27 edges, and 9 vertices.

Orthogonal projection

See also

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

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". Glossary for Hyperspace. Archived from the original on 4 February 2007.
  • 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