Lexors are analogues and structurally identical to chapters and, likewise, are numbered from 1 to 114. A chp and a lexor of the same number share the same name and tetron, but would diverge afterward in their subsequent numbered verses and lengths. For instance, Lexor 1, having the same name as chp 1, begins with the same (numbered tetron) 1:1, at which point the similarity ends as the two differ in their following verses and lengths. Similarly, their qupode duals, chp 9 and Lexor 9 (sharing the same name) are structurally identical as neither one has a tetron. They differ, however, in verses and lengths. This continues with the remaining pairs of chps and lexors, 2 - 8 and 10 - 114, with common names and tetrons 2:0 - 8:0 and 10:0 - 114:0, but distinct, otherwise.
Although, the lexors are identically structured with their counterpart chps, their verses are not in a naturally ascending order as it is with chps. Since the verses in any given lexor are assembled from different chps through the biflection actions they do not share a common link. Specifically, the verses in any given chp c are of the form: c:0 (except for chps 1 and 9), c:1, c:2, c:3, etc., all with the same c in common. In contrast, the verses in a lexor l are of the form l:0 (except for lexors 1 and 9), c1:v1, c2:c2, c3:v3, etc., where ci's are different and vi's do not follow any particular ordering. A natural ascending order among the lexor verses, however, can be established, as follows. The tetron is naturally designated as l:0, like in chps. The numbered verses are then labeled in ascending order from the tetron as l:1, l:2, l:3, etc., down to the last verse. Thus, l:1 corresponds to c1:v1, l:2 to c2:v2, l:3 to c3:v3, and so on. This labeling of verses according to their positions within the lexors will be referred to as reves, thereafter. Thus, reves display the inherent ordering of verses natural to lexors. Reves are to lexors as verses are to chps.
Since, all verses participate in the (co)bif scheme, the total number of verses in all lexors is the same as in chps. This establishes a ono-to-one correspondence between verses and reves. Given a lexor l, its tetron l:0 (the same as c:0) is shared with chp c = l. Its numbered verses ci:vi are paired with l:i, for i = 1, 2, 3, etc. This defines an involution, the flectope. It exchanges verses and reves while preserving handedness. It is a map that labels verses according to their positions in lexors.
The set of all verses arranged in their natural ascending order from chp 1 to chp 114 defines the standard global ordering on verses. Dualy, the set of all reves arranged in their natural ascending order from lexor 1 to lexor 114 defines the standard global ordering on reves. The one-to-one correspondence between the two global orders on verses and reves calls for another involution, the monotope. It is an order preserving map, where increasing verses are mapped to increasing reves. It does not, however, preserve handedness.
The two involutions defined map elements of different types: they exchange verses and reves while preserving either handedness or ordering. The composition of the two involutions (one involution followed by another) produces a map of elements of the same type: either from verses to verses or reves to reves, an endomap, (a map from a set to itself). Let F and M be the flectope, and monotope, resp. Their composition, O = FM, first, maps a verse to a reve under M, then the reve is mapped to another verse under F. Hence, their composition, O (the orconion, thereafter) maps verses to verses. It is a permutation, but not an involution. The composition of two arbitrary involutions is not necessarily an involution, in general, unless the two involutions commute. That is if G and H are two commuting involutions, GH = HG, then their composition K = GH is an involution: KK = (GH)(GH) = G(HG)H = G(GH)H = (GG)(HH) = 1 × 1 = 1. (By definition, repeating an involution returns objects to original state, resulting in a trivial or the identity map.) Since, FM ≠ MF, their composition, O, is not an involution. The orconion correlates the standard ordering of verses according to chps to their dual ordering according to lexors. It does not preserve handedness or ordering among verses. Similar map can be defined on reves, as well. The orconion will occupy a central role in the further derivations of algebraic structures among verses and chps.