7 Critical Constants
7.1 Six Zone
3 auto
 |
= 1.0514622 | ||
 |
= 1.7013016 | ||
| cos𝜃 | = 0.4472136 | ||
| sin𝜃 | = 0.8944272 | ||
| tan𝜃 | = 2.0000000 | ||
sin |
= 0.5257310 | ||
cos |
= 0.8506507 | ||
tan |
= 0.6180339 | ||
7.2 Ten Zone
5 auto
 |
= 0.7136441 | ||
 |
= 1.8683446 | ||
| cosϕ | = 0.7453559 | ||
| sinϕ | = 0.6666666 | ||
| tanϕ | = 0.8944272 | ||
sin |
= 0.3568220 | ||
cos |
= 0.9341723 | ||
tan |
= 0.3819660 | ||
7.3 Ten Zone
7 auto
 |
= 1.1547005 | ||
 |
= 1.6329931 | ||
| cosX | = 0.3333333 | ||
| sinX | = 0.9428090 | ||
| tanX | = 2.8284271 | ||
sin |
= 0.8164965 | ||
cos |
= 0.5773502 | ||
tan |
= 0.7071067 | ||
8A line radii of an icosahedron with edge = C. The pair of radii outline one end of a golden diamond.
11 B line radii of dodecahedron with edge = C. One pair outlines one end of the skinny diamond; another pair outlines an end of a maraldi diamond.
| A | = 0.9510565 C = cos18° C | |||||
| A | = 1.0981855 B | |||||
| B | = 0.8660254 C = cos30° C | |||||
| B | = 0.9105930 A | |||||
| C | = 1.0514622 A | |||||
| C | = 1.1547005 B |
7.4 The Appearance of the CTn Series in the Dimensions of the Triacontahedron and the Enneacontahedron
16Both these patterns can be found as sub patterns of the five-fold symmetry patterns of page.
18 All edges are A lines—one A line is perpendicular to the plane of page.
20 All edges are B lines— Aline is perpendicular to the plane of page.