Principles of Mathematics in Operations Research

244 Solutions

7

j-

/

~%i.i.-i)

i /

/v,-',-D

j f(0,f',-«

(-•,0,-f') (t,0,-f'>

f*7^

RS^—™~™™™™™-T«™™| ^

/ It/

r 1 * /

#7 ' *

* * I / *

***'*, ,/^\. V

/ r«

/ l

L* ?~ZZZJL~~««~^^

*ff

Fig. S.10. The dodecahedron, 0: golden ratio

7.6 See Figure S.10.

The polyhedron vertices of a dodecahedron can be given in a simple form

for a dodecahedron of side length a = \/b - 1 by

(0,±r\±</>f, (±^,0,±<A-^1 )T, (±<T\±^0)Tand(±l,±l,±l)T;

where <j> — ^^- is the golden ratio. We know (f> - 1 = ^ and 0 = 2 cos f. See

Figure S.ll.