Axial System of the Dodecahedron and Icosahedron. 
angle 
Distances 
angle 
Azimuths 
cosA 
cos Y 
cos Z 
Rot. Symbols 
cos 
sin 
cos 
sill 
1 
6 5-axes, ¿Rot. angle =36°, cos = 
Vs + l . V(!0 - 2 Vô) 
~ 4 ’ 8in 4 * 
31°44' 
2 
Vo - 1 
0° 
1 
0 
Vs -1 
+ 2 
Vs+1 Vs -1 . 
—T +—r-* + 4* 
v/(10-2n/5) 
V(io - 2 VS) 
V(i0- 2V5) 
0 
V(10-2Vs) 
9 9 
” 
>5 
180° 
-1 
0 
- 
9 9 
+ 99 
VS+i VS-i. ,, 
4 - 4 * + i* 
58°17' 
V(10 - 2 Vs) 
2 Vo 
V(10 + 2V5) 
2 V 5 
90° 
0 
i 
0 
VUO + 2V5) 
+ 2 V3 
+ V(10-2V5) 
2 VS 
•n/ö +1 1 . — 1 
-r- + *' + -r-* 
9 9 
» 
99 
270° 
0 
-i 
.. 
~ 99 
+ >> 
\^5 +1 , . \/'5 — 1 7 
“4 iJ+T-* 
90° 
0 
1 
31°43' 
( V(10 + 2Vo) 
VU0-2V5) 
( V(10 + 2 VS) 
2 VS 
V(io - 2 Vs) 
2s^5 
0 
Vs +1 .. VS -1. 
2 V5 
2 V5 
4 + i ,+ 4 
99 
99 
99 
148°17' 
- 
+ >> 
9 9 
+ 
” 
VS+i ,. VS-i. 
~T~ -> 1+ - A~- 1 
10 3-axes, g Rot. angle = 
60°, cos=£, sin = 
WS. 
5 4° 44' 
1 
Vb 
V2 
Vb 
45° 
1 
Vi 
1 
+ V2 
1 
+ Vb 
+ A 
Vb 
! 
+ Vs 
h (1+i+j+k) 
” 
>> 
»» 
135° 
9 9 
- ,, 
+ „ 
+ )) 
a (1 ~ * +j + k) 
99 
» 
” 
225° 
- >’ 
- » 
- » 
- ,, 
+ ,, 
h(l-i-j + k) 
” 
VS+1 
VS-i 
315° 
+ 
- >. 
+ 
- „ 
+ 99 
2 (1 + * —j + k) 
20°55’ 
90° 
0 
1 
0 
Vs -1 
VS+i 
. VS -1. VS +1 , 
2\/3 
2 V3 
+ 2V3 
+ 1— 
2V3 
i + — Í+-4- 1 ' 
” 
” 
» » 
270° 
0 
- 1 
0 
99 
+ „ 
, VS-i. VS+i, 
i- 4 3 + 4 h 
69°5' 
VS-1 
2 Vs 
VS + i 
2 Vb 
0° 
1 
0 
VS+i 
+ 2V3 
0 
V5 — 1 
+ T= 
2 Vb 
VS+1. Vs — 1, 
è+ 4 Í+ 4 k 
99 
99 
» 
180° 
- 1 
0 
- ” 
0 
+ » 
, VS+i. VS-i, 
■ \—— l+—^-k 
90° 
0 
i 
69°5' 
V5-1 
+ ivf 
+ Vs+i 
2 Vb 
VS-i 
+ 2 VS 
VS+i 
2 VS 
0 
. . Vs-i., VS+i . 
i+—. + —J 
” 
’’ 
9 9 
110°55' 
- » 
+ 99 
~ 9 9 
+ „ 
0 
. VS-i. VS+i. 
2- -4-* + — J 
CO 
■Ni 
Cn 
534 NOTES ON POLYHEDRA.