Göttingen Collection of Mathematical Models and Instruments

Cube with inscribed cuboctahedron

Model 485

 Category:

Description

Cube with inscribed (6 + 8) - plane polygon with 4·3 vertices. Polar figure of the the rhombus dodecahedron.

Cube The cube is one of the five Platonic solids, see also model 702.

Inscribed (6+8)-plane polygon with 4 · 3 vertices The solid inscribed in the cube is a cuboctahedron. The cuboctahedron arises from the cube by truncating its vertices. By truncating the vertices to the middle of the edges eight new triangles are created and the previously existing squares are transformed to six smaller squares. The cuboctahedron is circumscribed by

6 squares + 8 triangles = 14 faces.

It has 4·3 = 12 vertices and 24 edges. At each vertice two triangles and two squares are meeting (3,3,4,4).

rhombic dodecahedron The cuboctahedron is polar (dual) to the rhombic dodecahedron, see also model 925. To create this new solid a sphere is inscribed in the cuboctahedron such that the sphere touches each of the faces in exactly one point. These points of contact create the vertices of the dual solid. By connecting these 14 vertices 12 rhombi are formed. These rhombi are the faces of the rhombic dodecahedron. The number of edges remains the same during the transformation into the dual solid, while the number of vertices and faces is exchanged.

There are 11 Archimedean solids in the collection.

 472 Truncated tetrahedron inscribed in a tetrahedron 473 Truncated octahedron inscribed in an octahedron 474485 Cuboctahedron 474 inscribed in an octahedron485 inscribed in a cube 475 Truncated cube inscribed in an octahedron 476 Rhombicuboctahedron inscribed in a cube 478 Truncated icosahedron inscribed in an icosahedron 479 truncated dodecahedron inscribed in a dodecahedron 480481 Icosidodecahedron 480 inscribed in a dodecahedron481 inscribed in an icosahedron 482 Rhombicosidodecahedron 483 Snub dodecahedron 484 Truncated cube inscribed in a cube

The truncated icosidodecahedron and the lost truncated cuboctahedron are not included in the collection.

Showcase of this model is Case number 20