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Convex polytope constructed recursively
geometry, a Hanner polytope is a convex polytope constructed recursively by Cartesian product and polar dual operations. Hanner polytopes are named after
Hanner_polytope
Swedish mathematician
In a 1956 paper, Hanner introduced the Hanner polytopes and the Hanner spaces having these polytopes as their metric balls. Hanner was interested in
Olof_Hanner
Four-dimensional analogue of the cube
labels it the γ4 polytope. The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope. The construction
Tesseract
5-dimensional hypercube
deleting alternating vertices of the 5-cube, creates another uniform 5-polytope, called a 5-demicube, which is also part of an infinite family called the
5-cube
dimensions, and more generally, all Hanner polytopes. In 1969 Peter McMullen showed that every centrally symmetric 0/1-polytope is linearly unique. In the same
Projectively_unique_polytope
Convex regular 5-polytope in geometry
In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron
5-orthoplex
Maths conjecture
every Hanner polytope has exactly 3d faces. If Kalai's conjecture is true, these polytopes would be among the centrally symmetric polytopes with the
Kalai's_3^d_conjecture
6-dimensional hypercube
being a 6-dimensional polytope constructed from 12 regular facets. Acronym: ax It is a part of an infinite family of polytopes, called hypercubes. The
6-cube
Geometric prism
Triangular antiprismatic prism Triangular antiprismatic hyperprism It is a Hanner polytope with vertex coordinates, permuting first 3 coordinates: ([±1,0,0];
Octahedral_prism
4-D object; direct sum of a cube and a segment
octahedral prism. Being convex and regular-faced, it is a CRF polytope. It is a Hanner polytope with coordinates: [2] (0, 0, 0; ±1) [8] (±1, ±1, ±1; 0) Tetrahedral
Cubical_bipyramid
Four-dimensional analog of the octahedron
convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described
16-cell
Solid with six equal square faces
{\displaystyle \max\{|x-x_{0}|,|y-y_{0}|,|z-z_{0}|\}=a.} The cube is a Hanner polytope, because it can be constructed by using the Cartesian product of three
Cube
Solid with eight equal triangular faces
segments. More generally, every cross-polytope and its dual, hypercube, in any higher-dimensional space are Hanner polytope. The polyhedral compounds, in which
Regular_octahedron
Number associated with symmetric convex bodies
minimum known Mahler volume are hypercubes, cross polytopes, and more generally the Hanner polytopes which include these two types of shapes, as well as
Mahler_volume
Three raised to an integer power
elements. In polyhedral combinatorics, the hypercube and all other Hanner polytopes have a number of faces (not counting the empty set as a face) that
Power_of_three
Regular 6 dimensional polytope
In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell
6-orthoplex
to the number of faces of a Hanner polytope; see Kalai, Gil (1989), "The number of faces of centrally-symmetric polytopes", Graphs and Combinatorics,
Signed_set
Recursively-formed graph with two terminal vertices
if there are no R-nodes in its SPQR tree. Threshold graph Cograph Hanner polytope Series-parallel partial order Eppstein, David (1992). "Parallel recognition
Series–parallel_graph
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