18 



ON THE SECTIONS OF A BLOCK OF EIGHTCELLS 



Table of results von case III , 



tang <p = \]/?> , tang ^ = |-J/l4 , a = \}/^l 



G, 



c 2 c; 



V 3 B t - 



tt, w 



+ 6, 



B,C, 



B 3 B 3 ' 



(0, 1) 



— G, 



C/B 3 ' 



B 3 B 3 ' 



(1, 0) 



Go 



G, B 4 ' 



B, B„' 



(1,0) 



+ G, ; 



B 2 C 2 



B S B„' 



Co,*) 



— G e ' 



c;b.; 



B. b.; 



(i, o) 



G.' 



B„ C.' 



1\ li x ' 



(0, i) 



+ G 3 



c, c 2 



B,** 



(*j H 



-6.' 



C.'C,' 



b;^' 



(*, H 



G 3 



c 2 B„ 



B, B u 



(1,0) 



+ G, 



C.B, 



.1 B 3 



(i, o) 



-G,' 



».'$' 



B.'A' 



(0, i) 



e.' 



1\'C,' 



B*'Bi' 



(0, I) 



















So if we represent the really different pieces (1, ^), (4-, 0), 

 (£, 0) by A, B, C we find: 



G 7 , -j- G 3 , 

 G 6 , + G v 

 G e ', -f- G 6 , 

 G,, 

 G 3 ', -\- G 7 



<V 

 G„ 



(I I) 



* 0) 

 (0,1) 



* 0) 

 (0,f) 



13 pieces A 



20 



20 



B 



a 



59 pieces altogether 



So in case III 59 of the 81 eightcells are cut. 



15. In the following table giving the results for the seven cases 

 considered Q, O, T, H, P denote respectively cube, octahedron, 

 tetrahedron, hexagonal prism, triangular prism, whilst A, B, C, 

 I), I'J represent less regular sections oi' eightcells. 



