In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron. As a parallelohedron, the rhombic dodecahedron can be used to tesselate its copies in space creating a rhombic dodecahedral honeycomb.

The rhombic dodecahedron is the convex hull of the cube-octahedron compound and the first cuboctahedron stellation. If the rhombic dodecahedron is hinged into six square pyramids along three consecutive face diagonals, the resulting model can be folded into a cube (Wells 1991).

The rhombic dodecahedron is one of the 13 Catalan solids. It has 12 rhombi as faces, with 6 order-4 and 8 order-3 vertices. It is the dual of the uniform cuboctahedron. It can also be obtained as the convex hull of a cube and an octahedron scaled so that their edges are orthogonal.

The rhombic dodecahedron (hereinafter, referred to as r.d.) is a semi-regular polyhedron, in that all of its edges are the same length, yet the angles of its faces differ. Because each face is a parallelogram, there are 2 distinct angles for each face, one which is bisected by the long axis, with an angle less than 90 degrees, the other ...

It consists of copies of a single cell, the rhombic dodecahedron.All faces are rhombi, with diagonals in the ratio 1: √ 2.Three cells meet at each edge. The honeycomb is thus cell-transitive, face-transitive, and edge-transitive; but it is not vertex-transitive, as it has two kinds of vertex.Each vertex with the obtuse rhombic face angles is shared by 4 cells; each vertex with the acute ...

The Rhombic Dodecahedron inside its dual, the cubeoctahedron (wireframe). Its 4-edged vertices touch the midpoints of the cubeoctahedron faces. The length of the long diagonal of the rhombic faces equals the distance between the midpoints of neighboring square faces of the cubeoctahedron.

May 25, 1999 · The Dual Polyhedron of the Cuboctahedron, also sometimes called the Rhomboidal Dodecahedron (Cotton 1990). Its 14 vertices are joined by 12 Rhombuses , and one possible way to construct it is known as the Bauspiel .

Polyhedron - Rhombic dodecahedron detailed assembly diagram. Download a shape net of a polyhedron for DIY. Mathematical properties of the polyhedron. How many faces? Polyhedra shape net.

The rhombic Dodecahedron shares its 14 vertices with that of 14 vertices of the “120 Polyhedron (Type III: Dennis)”. The pattern of these 14 vertex coordinate numbers is

Aug 5, 2023 · Rhombic dodecahedron created by subdividing a cube into six identical pyramids and rotating them 180° so that their apexes point outward. The long and short diagonals of the rhomboid faces define a regular octahedron and cube respectively.