Uniform 3-4 duoprisms Schlegel diagramsTypePrismatic uniform polychoronSchläfli symbol{3}×{4}Coxeter-Dynkin diagramCells3 square prisms,4 triangular prismsFaces3+12 squares,4 trianglesEdges24Vertices12Vertex figureDigonal disphenoidSymmetry[3,2,4], order 48Dual3-4 duopyramidPropertiesconvex, 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 Net3D projection with 3 different rotationsSkew 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 34, order 12.Coxeter, H. S. M.; Regular Complex Polytopes, Cambridge University Press, (1974).
Related polytopes The birectified 5-cube, has a uniform 3-4 duoprism vertex figure:
3-4 duopyramid 3-4 duopyramidTypeduopyramidSchläfli symbol{3}+{4}Coxeter-Dynkin diagramCells12 digonal disphenoidsFaces24 isosceles trianglesEdges19 (12+3+4)Vertices7 (3+4)Symmetry[3,2,4], order 48Dual3-4 duoprismPropertiesconvex, 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 projectionVertex-centered perspective
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, (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-Strauss, The Symmetries of Things 2008, (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
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