Blended octahedron

From Polytope Wiki
Jump to navigation Jump to search
Blended octahedron
Rank3
Dimension4
TypeRegular
Notation
Schläfli symbol
Elements
Faces8 skew triangles
Edges24
Vertices12
Vertex figureSkew square
Petrie polygons8 skew hexagons
Related polytopes
ArmyOpe
Petrie dualBlended Petrial octahedron (abstractly equivalent)
SkewingSkew octahedron
Convex hullOctahedral prism
Abstract & topological properties
Flag count96
Euler characteristic-4
Schläfli type{6,4}
OrientableYes
Genus3
Properties
SymmetryB3×A1, order 96
ConvexNo
Dimension vector(2,3,3)

The blended octahedron, or skew octahedron, is a regular skew polyhedron in 4D Euclidean space. It is the result of blending an octahedron with a dyad.

PointDyadTriangleHexagonPetrial octahedronOctahedronSkew hexagonSkew triangleHexagonal-triangular coilBlended octahedronBlended Petrial octahedronSkew hexagonal-triangular coil
Symmetric realizations of {3,4}◊{}. Click on a node to be taken to the page for that realization.

The blended octahedron and its Petrie dual, the blended Petrial octahedron are realizations of the same abstract regular polytope, however they are not equivalent.

This underlying abstract polytope has faithful symmetric realizations, including the blended octahedron and its Petrial, however it has no pure faithful symmetric realizations. That is, it cannot be expressed without a blend or coincident vertices.

External links[edit | edit source]