Manuscript VII-E@1 · VII-E.tex · section · b713cf3c

A compact collar

One certified four-face slicing exchange › A compact collar · lines 2154–2185

VII-E@1#eq:hexagon, VII-E@1#eq:collar-transition

There are four core faces inside $R_{s}$ . Partition $K ∖ R_{s}$ into four resting collar polygons. The north-east polygon has counterclockwise spatial vertices

(X_{s}, 0), (R_{x}, 0), (R_{x}, R_{y}), (0, R_{y}), (0, Y_{s}), (X_{s}, Y_{s}) .

The other three are reflections, ordered counterclockwise. Every collar vertex has $T = H + s$ . The inner and outer side midpoints divide each rectangular boundary into eight segments. These coplanar subdivisions are part of the declared cell interface.

For affine pairs, use

(L, b) z = L z + b, (L, b) (L^{'}, b^{'}) = (L L^{'}, L b^{'} + b) .

The collar chart is

A_{0} (z) = z - H e_{0} = (T - H, x, y) .

The core chart is $A_{i} = (C_{i}, 0)$ , so a core-to-collar transition is

A_{0} A_{i}^{- 1} = (C_{i}^{- 1}, - H e_{0}) .

Collar-to-collar transitions are identities.

Displayed formulas in this passage

VII-E@1#eq:hexagon · line 2159
$(X_{s}, 0), (R_{x}, 0), (R_{x}, R_{y}), (0, R_{y}), (0, Y_{s}), (X_{s}, Y_{s}) .$
VII-E@1#eq:collar-transition · line 2180
$A_{0} A_{i}^{- 1} = (C_{i}^{- 1}, - H e_{0}) .$
unlabeled · line 2171
$(L, b) z = L z + b, (L, b) (L^{'}, b^{'}) = (L L^{'}, L b^{'} + b) .$
unlabeled · line 2176
$A_{0} (z) = z - H e_{0} = (T - H, x, y) .$

A compact collar

Displayed formulas in this passage

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