Trapezo-rhombic dodecahedral honeycomb
Encyclopedia
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| Type | convex uniform honeycomb Convex uniform honeycomb In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.Twenty-eight such honeycombs exist:* the familiar cubic honeycomb and 7 truncations thereof;... dual |
| Cell type | trapezo-rhombic dodecahedron Trapezo-rhombic dodecahedron The trapezo-rhombic dodecahedron is a convex polyhedron with 6 rhombic and 6 trapezoidal faces.This shape could be constructed by taking a tall uniform hexagonal prism, and making 3 angled cuts on the top and bottom... VG3.4.3.4 |
| Face types | rhombus Rhombus In Euclidean geometry, a rhombus or rhomb is a convex quadrilateral whose four sides all have the same length. The rhombus is often called a diamond, after the diamonds suit in playing cards, or a lozenge, though the latter sometimes refers specifically to a rhombus with a 45° angle.Every... , trapezoid Trapezoid In Euclidean geometry, a convex quadrilateral with one pair of parallel sides is referred to as a trapezoid in American English and as a trapezium in English outside North America. A trapezoid with vertices ABCD is denoted... |
| Symmetry group Symmetry group The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation... |
P63/mmc |
| Dual | gyrated tetrahedral-octahedral honeycomb Gyrated tetrahedral-octahedral honeycomb The gyrated tetrahedral-octahedral honeycomb or gyrated alternated cubic honeycomb is a space-filling tessellation in Euclidean 3-space made up of octahedra and tetrahedra in a ratio of 1:2.... |
| Properties | edge-uniform, face-uniform, cell-uniform |
The trapezo-rhombic dodecahedral honeycomb is a space-filling tessellation
Tessellation
A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art...
(or honeycomb
Honeycomb (geometry)
In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions....
) in Euclidean 3-space.
It consists of copies of a single cell, the trapezo-rhombic dodecahedron
Trapezo-rhombic dodecahedron
The trapezo-rhombic dodecahedron is a convex polyhedron with 6 rhombic and 6 trapezoidal faces.This shape could be constructed by taking a tall uniform hexagonal prism, and making 3 angled cuts on the top and bottom...
.
It is similar to the more symmetric Rhombic dodecahedral honeycomb
Rhombic dodecahedral honeycomb
The rhombic dodecahedra honeycomb is a space-filling tessellation in Euclidean 3-space. It is the Voronoi diagram of the face-centered cubic sphere-packing, which is believed to be the densest possible packing of equal spheres in ordinary space .It consists of copies of a single cell, the rhombic...
which has all 12 faces as rhombi.