8a.Truncated icosahedron 12/5 20/6 from truncation of icosahedron 20/3

Data

The distance from the center of the icosahedron to the center of the icosahedron triangle is EP 0.76. The distance from

the center of the truncated icosahedron to the center of the hexagon is EA 2.27 . These two distances are equal, thus EA

= EP 1/3.

Construction

EP is divided in three equal parts.

20 hexagons (red) are applied on the icosahedron triangles. The twelve coners (yellow) are cut off,

resulting in twelve pentagons (green-blue).

Line 1. Icosahedron, net and solid. .

Line 2. Truncated icosahedron, net and solid

8b. Truncated icosahedron from truncation of dodecahedron 12/5

Data

The distance from the centre of the dodecahedron to the center of the pentagon is E_P1.11. The distance from

the centre of the truncated icosahedron to the centre of the pentagon is EA ×2.33

These two distances are equal, thus EA = EP 0.48

. The distance between the corner of the truncated icosahedron pentagon (red) and

the midpoint of the dodecahedron pentagon is incircle radius of the dodecahedron pentagon minus circum-circle radius

of the truncated icosahedron pentagon ; Ep 0.69 minus EA 0.86 = EP0.28.

Construction

The pentagons (red) are applied on the dodecahedron pentagons with the corners directed to

the midpoint of the dodecahedron pentagon edges

The twenty corners (yellow) of the dodecahedron are cut off, resulting in twenty hexagons (green-blue.

Drawing demonstrating the site of the truncated icosahedron pentagon