the angles of crystals. 127 
permutation is allowed may be distinguished from those 
where it is not, by separating the letters />, 7, r in the former 
case by a comma, and in the latter by a semicolon. The 
other co-existent planes in each primary form will be seen in 
the following table. 
Table of planes which exist if (/> ; 7 ; r) exist. 
In the rhomboid _ - , _ 
{p> 9. 
The doubly-oblique prism 
ip;q 
; r) 
The oblique rhombic prism 
{Py 9: 
' 
The oblique rectangular prism 
{p',±q\ r) 
The right oblique-angled prism 
i±P'y 
±q'r r. 
The right rhombic prism 
{±Py 
± 9 ; '') 
The right square prism 
+ 9; r ) 
The cube _ _ _ _ 
/+ ^ 
+ 
( 
±9.'-) 
The regular tetrahedron and regular oc- 
tahedron - - _ 
(/. < 7 . '■) 
{py p — Hyp — r) 
{(t—py </. 9 — '■) 
[r—p, r—q, r) 
The direct symmetrical tetrahedron and 
square octahedron 
{p ; 9 . 0 
{P'yp—r,p — q) 
(9 — 9 > 9— /) 
[r—qy, r — p, r) 
The inverse symmetrical tetrahedron 
and rhombic octahedron. 
(/> ; 9 ; '•) 
{p'yp — r-,p — q) 
{q — nq;q—p) 
{r — q-, r—p-,,) 
