679] 
ON THE REGULAR SOLIDS. 
273 
I add for greater completeness the following results, some of which were used in 
the calculation of the foregoing table. Considering successively (1) the tetrahedral 
triangle, summits 3 points B, centre a point B ; (2) the hexahedral square, summits 
4 points B, centre a point © ; (3) the octahedral triangle, summits 3 points ©, 
centre a point B ; (4) the icosahedral triangle, summits 3 points A, centre a point 
B ; (5) the dodecahedral pentagon, summits 5 points, centre a point B ; and (6), 
what may be called the small pentagon, summits 5 points <3> lying within a dode 
cahedral pentagon, and having therewith the common centre B ; we may in each case 
write s the side, r the radius or distance of the centre from a summit, p the 
perpendicular or distance of the centre from a side. And the values then are 
s 
r 
P 
Tet. A 
109° 30' 
70° 30' 
54° 45' 
Hex. square 
70 30 
54 45 
45 
Oct. A 
90 
54 45 
35 15 
Icos. A 
63 26 
37 22 
20 55 
Dod. pentagon 
41 50 
37 22 
31 43 
Small pentagon 
15 30 
13 16 
10 48