10 a. Snub cube 32/3 6/4 from truncation of cube 6/4

Data

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

The distance from the centre of the snub cube to the centre of the square (red) is EA×1.14.

These two distances are equal, thus EA = EP×0.44.

The short distance between the original cube edge and the corner of the snub

cube square (red) is EP×0.23. The long corresponding distance is EP×0.35. (According to

Badoureau)

Construction

The six squares (red) are applied on the six cube squares. The corners(yellow) are cut off,

resulting in 32 triangles (green-blue)

Line 1: Cube, net and solid. Line 2: Snub cube, net and sold

10b. Snub cube from truncation of octahedron 8/3

Data

The distance from the centre of the octahedron to the centre of the triangle is EP×0.41.

The distance from the centre of the snub cube to the triangle (red) is EA×1.21.

These two distances are equal, thus EA = EP×0.33.

10c. Snub cube from truncation of truncated cuboctahedron 12/4 8/6 6/8

The diagonals (red) on the squares,hexagons and octagons are, however, not of the same

length. Thus, the edges of the snub cube (red) are not equal and the snub cube is not a correct.

Archimedean polyhedron

10d. Snub cube by transformation of the small rhombicuboctahedron (32 triangles and 6 squares)

The small rhombicuboctahedron is made as a “jitterbug” construction. This is twisted in order to change

12 squares into rhombi (diagonal ratio: 1/Ö3, the short diagonal = the edge). These are divided in 24 equilateral

triangles. The twisting can be made in two directions, giving leuvo-and dextro-forms.