238 
Proceedings of the Royal Society 
The form hhl, where + A: + ? = o is a twelve-sided prism, whose axis 
is parallel to the optic axis. 
It is a combination of the following forms of the prismatic 
system - 
1 h-l 2h-k-l 
where = = ^ 
l-h 
2 ’ 
2k-I-h 
h — k ^ 2l — h — k 
Ex . — The form 312 is a combination of 210, 130, 510. 
10. The form hkk is a rhomhohedron. 
It can be shown that the rhombohedra 
hkk, 
andlA: — 7i, 2h-\-k, 21i-\-k, 
are inverse with respect to each other. 
A combination of these rhombohedra is a combination of the 
following forms of the prismatic system — 
3a a 2/3 ; 0 a 
where a — li-k p=2k-^h. 
Ex . — A combination of the rhombohedra 100 and 122 (which are 
inverse with respect to each other), is a combination of the forms 
312 and 011 of the prismatic system. 
The rhombohedron hkk itself is a combination of two hemihedral 
forms with parallel faces, viz., — 
7T 3a a 2/3 and tt oa/3, 
wljere a and (S have the same values as above. 
11. The form hkl, where h,k,l are connected by none of the pre- 
ceding relations, is sometimes termed a scalenohedron. 
It can be shown that the following scalenohedra are inverse with 
respect to each other, viz., — 
hkl 
and 2k + 21 - It, 21 -h 2h - k, 2h -f 2k - 1. 
