132 
EEV. T. P. TCTEKMAN OF THE THEOEY OE THE POLTEDEA. [§ 1. XVII. 
triarch axines, in all of which, except the first, only half the solid is seen, the rest being 
conceived as below the page, which is a zonal plane. The dotted lines are undrawn 
zonal traces, which are, however, not all exhibited. 
The zonal signatures are (art. XV.), — 
A. z={( . . )(4.yo-}, z,= {(4.i;)(2.i,)or}; 
B. z={(4.1,)( . . )0r}, Z,= {(2.1,}(4.i;)0-"}. 
These two are reciprocals, both regular polyedra. 
C. Z={(4.1,+4.i;)(..)0"'}, Z,= {(2.1,-l-4.i;+2.i;)(4.1J0"''}; 
D. Z={(4.1,)(. .)0r"}, Z,= {(2.1,+4.i;)(4.1)0-"0^->'}; 
E. z={(4.i,}(4.i;)}, z,= {(2.i,+4.i;)(2.i;)0-'}. 
The sohd C has only amphigonal axes, and has eight non-polar edges in Z, all aHke, 
and four non-polar faces, and four non-polar edges, in Z^ either all ahke. D has prin- 
cipal and secondary amphigonal, and tertiary amphigrammic, axes. The 12-edron E has 
principal and secondary amphigonal and tertiary amphiedral axes. Four of the six prin- 
cipal polar summits are in the plane of the page. The principal poles of E are tessaraces ; 
the eight secondary poles are triaces ; the twelve tertiary poles are quadrilaterals. 
None of the solids drawn have zoneless faces, but they may have any number, if we 
load each of the forty-eight interzonal regions with the same polyedron R, zoned or zone- 
less. If R is zoneless, we shall impose R twenty-four times and its refiected image twenty- 
four times, so that the traces may be all preserved. The polyedron R may be polar or 
not, and symmetrical or not. 
What precedes is sufficient to show that our signatures accurately record the zonal 
configuration. What more is required for placing the polyedron upon record, we shall 
see when we treat of registration. 
