11a. Small rhombicosidodecahedron 12/5 20/3 30/4 from truncation of icosahedron 20/3

Data

The distance from the centre of the icosahedron to the centre of the triangle is EP×0.76

The distance from the centre of the small rhombndicosidodecahedron to the centre of the

triangle (red) is EA×2.16. These two distances are equal, thus EA = EP×0.35.

Circum-circle radius of icosahedron triangle is EP 0.58

Circum-circle radius of rhombicosidodecahedron triangle (red) is EA 0.58.

The distance between the corner of the small rhombicosidodecahedron

triangle (red) and the corner of the icosahedron triangle is EP 0.58 minus E_A 0.58 = E_P 0.38.

Construction

Twenty triangles (red) are applied on the icosahedron triangles.

The twelve corners (yellow) are cut off, resulting in 12 pentagons (green-blue). The thirty edges are cut

off, resulting in thirty squares (green-blue)

Line1: Icosahedron, net and solid.

Line 2: Small rhombicosidodecahedron, net and solid

11b. Small rhombicosidodecahedron from truncation of dodecahedron 12/5.

Data

The distance from the centre of the dodecahedron to the centre of the pentagon is EP×1.11

The distance from the centre of the small rhombicosidodecahedron to the centre of the

pentagon (red) is EA×2.06. These two distances are equal, thus EA = EP×0.54.

The circum-circle radius of dodecahedron pentagon (EP×0.85) minus the circum-circle

radius of the rhombicosidodecahedron pentagon (red) (EA×0.85) is the distance between

the dodecahedron pentagon corner and the small rhombicosidodecahedron pentagon

corner, i.e, EP×0.39.

Construction

The rhombicosidodecahedron pentagons (red) are applied on the twelve dodecahedron

pentagons . The twenty corners (yellow) are cut off, resulting in twenty triangles (green-blue) The thirty

edges are cut off, resulting in thirty squares (green-blue).

Drawing demonstrating the application of

the rhombicosidodecahedron pentagon (red)

on the dodecahedron pentagon

.