rod

Part I, The Sentence and the Kernel · defined in Chapter I, The Founding Sentence

Of an anchored observer, one of the three letters through its anchor; the other three are its odd letters.

Plate W.12An observer anchored at report 0: its rods 01, 02, 03 in gold, one on each axis, and the odd letters 23, 13, 12 opposite them in blue.

With the anchor a line $L$ of the Fano plane missing the clock, the rods are the three points of $L$ , one on each axis, and the odd letters are the other three; Chapter X calls them the antirods, since each is the antipode of a rod. On $K_4$ the rods are the star of the anchor’s vertex and the odd letters the triangle opposite it. For the base observer $(1,246)$ the rods are 2, 4, 6 and the odd letters 3, 5, 7. The observer’s own symmetry, $H_x\cong S_3$ , can do nothing but permute its rods.

Two registers at one clock with different vantages share exactly one rod, the point where their lines meet, and the exchange rule is enabled exactly when their tops are that rod and its antipode. Around a closed loop of clock changes the re-description of a history returns up to a permutation of the three rods: the price of rulial relativity.

As mathematics

For an antiflag $(p,L)$ the rods are the points of $L$ and the odd letters the triangle $\mathcal P\setminus(L\cup\{p\})$ , three non-collinear points. Every non-collinear triple is the triangle of exactly one antiflag, since its complement contains exactly one line, so the twenty-eight observers are the twenty-eight non-collinear triples, and two observers meet exactly when their triangles are disjoint.

On $K_4$ the rods are the star of a vertex, which meets every axis once, and the odd letters the opposite triangle. In the crystal the three edges at a site of report type $v$ are the steps along the rods of $v$ , and every permutation of them extends to a symmetry of the whole realized net, coming from the stabilizer $S_3$ of $v$ .

Its name in another field	Bridge
the star of a vertex of $K_4$	built
for the odd letters, the triangle opposite it	built
the three edges at a site of the $K_4$ crystal	built

Built from: anchored observerletter
In the volume: IThe Founding SentenceIVWorld, Kernel, ObserverVFour Reports, Six LettersVIIISpace as a TallyXThe Finite Celestial SphereXIRulial RelativityXIIThe Coxeter GraphXVSpin from the Double CoverXIXRulial InvariantsXXThe Commuting SquaresXXINonfinite LimitsXXIIILight, Vacuum and Handedness