12 ON CERTAIN SERIES OF SECTIONS OF THE 



Here T (J" ^) == ƒ times the edge; r^ bisects (^ )A and (Z)' J r 

 divides (^'^^)(^i) in the ratio a: 1 — a. 



This gives the points (J^)^ A^, {A^^^ A^, {/B)„ {A J, {A'c\, (A^^), 



{A^B) (A B), {A'C)XAC). See on diagram IV tlie points (5, 4, 6, 8, 

 7, 2); 8 and 1 are the points {D' _X {!)' J. 



Again / A and -5' intersect in a phme through the point 

 {A'C) {A ) and parallel to {A ), {A ), {A _). This is shewn in pro- 

 jection in tig. 22. It gives the points {A ) (A (2), {A'C){A ), 

 (AJiAê), {/B) (A). 



fj D 



2 '' 



14. Let the 600-cell be cut by a space S^ in points {A B), {A B'), 

 UC), {A d) {Jb), {A if), {EC), {B C-),{C'D),{CD'),{B-D),{B]f); 

 it Avill be parallel to S . The line T\^ r , parallel to {B' ) /• and passing 



2 



through i^t'B), (tig. ID), is the projection of the intersection of /(^-^ ) 



aiid/S'\ Comparing this with the line F r , we have .-^ r =jöcand 



(i;'_.)F =;;«. 



This 'gives the points (J_)_ (J^,), (J^)^ (J J, {B\_XiA ê), ^){A Ö) 



(on plate V the points 4, 3, ü, 1 ; 5 and 2 are (A'B) and (J'6'), etc.). 



■i . . . '2 



The solid 7 A and iS_ intersect in a })lane passing through {A'B), 



{/C), (Jb) and this plane passes through {Aê)jA^^,{A(d){A ), 

 {Ay)y^), hg. 22. 



The space S\ and / è intersect in a plane through {B' ) (A^) that is 

 parallel to (Z)' ){B' ){B' ). This plane is projected in the line rr, tig. 20. 



Let f'{B' ) be called // times the edge and we have the points 

 (i>;p^/J^«), (B'^)^^ {S^(d), {B\)^^ (J-7). 



Again ;S] and I {A S) intersect in a plane through (B' _), {B' ), 



{A ^)i A , tig. 21. Here (X>'/;)A^ind a parallel plane through (A'B) (A'C) 



is projected in the line /• v giving A J' = c times the edge and 



{B'^) r = pf. Whence we have the points (.4 ) {A^J, {B' ) , S , {B' ) ,^ 



see list. 



In diagram F the zone on I A is 23, 5, 12, 2, lb, 13 and 



that on /J is 2, 7, 5, 8, Î), 1Ü, 11. 



1 



