Rhombic dodecahedral honeycomb

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Rhombic dodecahedral honeycomb
Rank4
TypeUniform dual
SpaceEuclidean
Notation
Bowers style acronymRadh
Coxeter diagramm3o4o *b3o ()
Elements
CellsN rhombic dodecahedra
Faces6N rhombi
Edges8N
VerticesN+2N
Vertex figureN cubes, 2N tetrahedra
Related polytopes
ArmyRadh
RegimentRadh
DualTetrahedral-octahedral honeycomb
Abstract & topological properties
OrientableYes
Properties
SymmetryS4
ConvexYes
NatureTame

The rhombic dodecahedral honeycomb, or radh, is an isotopic honeycomb with rhombic dodecahedron cells. It can be obtained as the dual of the tetrahedral-octahedral honeycomb.

Vertex coordinates[edit | edit source]

Vertex coordinates for a rhombic dodecahedral honeycomb of unit edge length can be given as:

  • ,
  • .

where i , j  and k  are even integers.

Multiplying these coordinates by gives integral coordinates for the rhombic dodecahedral honeycomb.

External links[edit | edit source]