3-4 duoprism

Stereographic projection of complex polygon, ₃{}×₄{} has 12 vertices and 7 3-edges, shown here with 4 red triangular 3-edges and 3 blue square 4-edges.

The quasiregular complex polytope ₃{}×₄{}, , in ${\displaystyle \mathbb {C} ^{2}}$ 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]

The birectified 5-cube, has a uniform 3-4 duoprism vertex figure:

3-4 duopyramid

3-4 duopyramid
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

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

• 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.

• 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