Table of the important parameters of a snub dodecahedron (an Archimedean solid having 80 congruent equilateral triangular & 12 congruent regular pentagonal faces each of equal edge length) such as normal distances & solid angles subtended by the faces, inner radius, outer radius, mean radius, surface area & volume calculated by using HCR's Theory of Polygon & Newton-Raphson Method. It can be used in analysis, designing & modelling of uniform polyhedra.

1. Analysis of Snub Dodecahedron (Archimedean solid): Let there be any snub dodecahedron
having 80 congruent equilateral triangular faces & 12 congruent regular pentagonal faces
each with edge length then all its important parameters are calculated as tabulated below
Congruent
polygonal
faces
No. of
faces
Normal distance of each face from
the centre of the snub dodecahedron
Solid angle subtended by each face at the
centre of the snub dodecahedron
(in Ste-radian (sr))
Equilateral
triangle
80
√ (√ )
Regular
pentagon
12
√
( √ )
(√
( √ )
)
Inner (inscribed) radius ( )
√
( √ )
Outer (circumscribed) radius ( )
Mean radius ( )
Surface area ( ) ( √ )
Volume ( )
(
√
√
( √ ) ( √ )
)
* When a solid snub dodecahedron (Archimedean solid) of the maximum volume is produced from
a solid sphere having certain diameter then approximate of total volume of the parent
sphere is removed as scraps in facing operations to generate 80 congruent equilateral triangular
& 12 congruent regular pentagonal faces each of equal edge length.
Estimated & illustrated by Mr Harish Chandra Rajpoot (B Tech, Mechanical Engineering)
M.M.M. University of Technology, Gorakhpur-273010 (UP) India Dec, 2014