PARTITIONS OF THE X-ACE AND THE X-GON. 61 
quadrant, and being read in one direction in two quadrants 
and in another in the other two; wherefore every con- 
structed configuration will be begun at four different points 
of the circuit, and appear in two results as the reflected 
image of itself seen in the other two. 
If then from the above number of arrangements of lines 
we subtract the doubly reversibles of Art. 15, twice the 
doubly irreversibles of Art. 16, and twice the reversibles of 
17 and 18, the remainder divided by four is the number of 
irreversibles here required. That is, 
4y—4 | 1 
TR2(4e +m +1,22) =1R?(4er + 1,22) {re MEL 
a—2|1 2r—2|1 
at o B30) hi 
m 
oz Gt) os 
ioe “2 ae: pen “2 
my Qr-2| 1 a m 221 ‘ 
wi 8) pp MARE) gs 
(eat 2Qa—2|1 
a. no 
— eee ee | 
Bird +1a5| St eet ea QF 
m a2 1 m 
zt) sy he LY) m4 
a 2 . Ae ee ee 2 2 
= ile z = yan 
piace 
2 ae 0 eT i 
|? {1 
which is part of the number I(4a-+m-+ 1,22). 
90, Prosiem J. To determine the number of triply re- 
yersible (6a -+m+ 1)-edra having 3z triangles. 
All these by the definition of a triply reversible, Art. 5, 
