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EEV. T. P. KIEKMAJ^ ON THE THEOEY OE THE POLYEDEA. [§ 1. Iil.-vi. 
III. a. Monozone polyedm.—A monozone polyedron has no symmetry but that of a 
single zone. It has the zonal signature 
Z={g, G, 0 “, on, 
which records that Z has g zoned summits, G zoned faces, a zonal edges, and h epizonal 
edges. 
No tioo AA' of the zoned features of a monozone jgolyedron have the same configuration^ 
or are one the reflected image of the other. 
For if A were identical in configuration with A', there would be a symmetry of repe- 
tition, not essential to the zone Z. And if A were the reflected image of A', there would 
be a zone different from Z, passing between A and A'. 
Every zoneless feature, B, is twice read on a monozone polyedron, viz. B and its reflected 
image. 
The undrawn lines of Z are the zonal traces of the zoned faces and summits. 
The trace of a zone is agonal, diagonal, or monogonal, according as it passes through 
one angle, two angles, or one angle only, of the face or summit. 
Monogonal traces are seen only in odd-angled faces or summits. 
A monozone 8-edron 12-acron is 
whose zonal signature is 
Z={2, 2 , 0 \ 0*}. 
IV. Zoned axis. — Any number of zonal planes may have a common hne or axis, which 
is a zoned axis. 
Def. An axis isjanal, whether it he zoned or zoneless, if the configuration C, or if the 
reflected image of C, which is read at one extremity of the axis, can be read by an 
opposite eye at the other extremity, by turning the axis through any angle. 
In particular, a j anal zoned axis is said to be ohjanal, when the configuration C read 
at one pole or extremity is the configuration C', read at the other pole (by an opposite 
eye in the axis), turned through two right angles, C' being C inverted. 
Also a janal zoneless axis is said to be contrajanal, if the configuration C read at one 
pole is the reflected image of the configuration C' which can be read by an opposite eye 
at the other. 
Def. An axis, whether zoned or zoneless, is heteroid, if the configuration C read at one 
pole cannot he read at the other, nor read inverted, nor reflected. 
V. According to the character of the polar features terminating an axis, zoned or 
zoneless, the axis is amphiedral, amphigonal, amphigrammic, gonogrammic, edrogrammic, 
or gonoedral, terms which explain themselves. 
An axis is m-zoned, when it is the intersection of m zones. 
A zoned amphigrammic, edrogrammic, or gonogrammic axis is of necessity two-zoned ; 
for a polar edge may be zonal in one zone, and epizonal in another, but cannot belong 
to a third. 
VI. Theorem. There are two different hemizonal sequences of configuration, and only 
two, read alternately upon the hemizones about a zoned axis. 
