9a. Truncated dodecahedron 12/10 20/3 - truncation of dodecahedron 12/5

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 truncated dodecahedron to the centre of the decagon (red) is

EA×2.49. These two distances are equal, thus EA = EP×0.45.

Alternative calculation of EA:

EP is divided in three parts : x + xF + x ; x = EP / (F + 2) ; EA = EP F / (F+2)=0.45 EP

(F = 1.618 , Golden section) .

Twelve decagons (red) are applied on the twelve original pentagons. The twenty corners (yellow)

are cut, off giving 20 triangles (blue-green).

Line 1: Dodecahedron, net and solid. .

Line 2: Truncated dodecahedron, net and solid

9b. Truncated dodecahedron – truncation of icosahedron 20/3

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 truncated dodecahedron to the centre of the triangle

(red) is EA×2.91. These two distances are equal, thus EA = EP×0.26.

Twenty triangles (red) are applied on the icosahedron triangles with the corners directed at

the midpoint of the triangle edges.The distance beween the corner and the mid-point is the

incircle radius of the icosahedron triangle minus circum-circle radius of the truncated

dodecahedron triangle (red).: 0.29 EP – 0.58 EA = 0.14 EP

The twelve corners of the icosahedron /yellow) are cut off, giving 12 decagons (green-blue).

Drawing demonstrating the site of the truncated dodecahedron triangles(red)