5a.Small rhombicuboctahedron 8/3 18/4 from truncation of cube 6/4

Data

The distance from the centre of the cube to the center of the square is EP/2.

The distance from the centre of the rhombicuboctahedron to the center of the square (red) is EA×1.21.

This two distances are equal, thus EA = EP×0.41

[Alternative calculation of EA: The edge of the cube is divided in three parts ; x + xÖ2 + x = E_P x = E_P /(2+Ö2) thus EA=xÖ2=EP×0.41]

The distance between the edge of the original cube square and the edge of the rhombicuboctahedron

square (red) is (E_P minus E_A )/ 2 = EP×0.30

Construction

The cube edge is divided in two parts: (x) near the corners and one part (xÖ2) between these two.parts.

The six squares (red) are applied on the six cube squares.

The twelve edges and the eight corners (yellow) of the cube are cut off, resulting in twelve triangles (green-blue) and

eight squares (green-blue).

If the faces of a cube are moved outwards to a distance of an edge between the edges a small rhombicuboctahedron is formed. The same

procedure for the octahedron gives the same result.

Line 1: Cube net and solid. A drawing for calculation of EA

Line 2: Rhombicuboctahedron , .

net and solid