256 
Proceedings of the Royal Society of Edinburgh. [Sess. 
With centre DO we have the icosahedron — 
BO; Cl, 2, 3, 4, 5; E 1, 2, 3, 4, 5 ; -DO; 
the dodecahedron — 
B 1, 2, 3, 4, 5 ; D 1, 2, 3, 4, 5 ; E 1, 2, 3, 4, 5 ; -Cl, 2, 3, 4, 5 ; 
and the icosahedron — 
A ; C 1, 2, 3, 4, 5 ; - D 1, 2, 3, 4, 5 ; -BO, 
and the last figure becomes a plane figure in the projection. 
With centre El we have the icosahedron — 
C3,4; D 0, 1 ; E 2, 5, 3, 4 ; - D 0, 1 ; - C 3, 4, 
the dodecahedron — 
BO, 1; C 2, 5, 3, 4 ; D 2, 5 ; E 3, 4, 31, 41 ; 
-BO, 1; -02,5,3,4; -D 2, 5; 
the icosahedron — 
B 2, 5 ; C 1, - 1 ; E 2, 5, 35, 42 ; - C 1, - 1 ; - B 2, 5 ; 
and the icosidodecahedron — 
A; B3,4, -3, -4; C 2, 5, - 2, - 5 ; D 3, 4, - 3, - 4 ; El, - 1,25,52; 
- A ; - B 3, 4, - 3, - 4 ; - C 2, 5, - 2, - 5 ; - D 3, 4, - 3, - 4, 
the latter being projected into a plane figure. 
§ 6. The equations of transformation for the stereographic projection 
with centre at the point A, i.e. the origin, and plane of projection w = 
2 (e + 1), are : 
x _ y _ z _ 2(e + 1) 
x' y z w' 
where x', y', z', w' are the co-ordinates of a vertex of the 600-cell and x, y, z 
those of its projection. 
Table I. — Notation for the 120 Vertices of the 600-cell, (a) Schoute’s 
Notation, ( b ) Notation used in the Present Paper. 
a. 
b. 
a. 
b. 
a. 
b. 
a. 
b. 
a. 
b. 
1 
E 
52 
13 
B 
0 
25 
B 
2 
37 
B 
3 
49 
E 
2 
2 
E 
1 
14 
B 
1 
26 
B 
5 
38 
B 
4 
50 
E 
5 
3 
E 
1 
15 
B- 
1 
27 
B- 
5 
39 
B- 
4 
51 
E 
4 
4 
A 
16 
-B 
0 
28 
-B 
2 
40 
-B 
3 
52 
E 
-3 
5 
C 
5 
17 
C 
1 
29 
D 
2 
41 
C 
5 
53 
E 
5 
6 
c 
2 
18 
C- 
1 
30 
D 
5 
42 
C 
2 
54 
E 
2 
7 
c 
4 
19 
C 
1 
31 
D- 
5 
43 
C- 
2 
55 
E 
42 
8 
c- 
-3 
20 
-c 
1 
32 
-D 
2 
44 
-c 
5 
56 
E 
53 
9 
-c 
5 
21 
D 
0 
33 
C 
4 
45 
D 
3 
57 
E 
3 
10 
c 
3 
22 
D 
1 
34 
c 
3 
46 
D 
4 
58 
E 
4 
11 
0- 
-4 
23 
D- 
1 
35 
c- 
3 
47 
D- 
■4 
59 
E 
41 
12 
-C 
2 
24 
-D 
0 
36 
-c 
4 
48 
-D 
3 
60 
E 
13 
