DC Marvel Comics - Batman & Spiderman by J M deMatteis

By J M deMatteis

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Their construction is far from being mathematically trivial. Jones, The Grammar of Ornament, London 1856 and A. Racinet, L'Ornement Polychrome, Paris 1869. On the Greek friezes 1/1,2,3 we recognize some principles on which the honeysuckle grows without finding any attempt a t imitation. The softly curved lines reflect grace and noble simplicity. The symmetry group of the friezes 1/1 and 1/2 is $2 a n ( i t h a t of 1/3 is %2. Egyptians used in their ornaments S- and C-shaped volutes, their native flowers and other elements which all had a symbolic meaning.

If AB is parallel or perpendicular to I, let a smallest translation of the group non-parallel to AB move A into C (Fig. 4/12). To determine the position of the point G, we consider the strip 8 bounded by the orthogonal bisector b of the segment AB and the parallel line a passing through A. Clearly, we may suppose, without loss of generality, t h a t G lies in or on the boundary of 8. If G is an inner point of S, we reflect G in Z, obtaining C". But then the composition of the translations A —>■ G and A -> C" or A -> G arid (7/ -> A would yield a translation of the group smaller than the translation A ~> B.

Since translations other than those transforming a triad into a triad are out of the question, we have only to consider, say, the translation P -> R. This translation followed by a third-turn about R transforms PR into RQ, showing t h a t the resulting motion would be a third-turn about the centre of PQR. This contradicts our previous result, according to which the lattice points are the οκΐν centres of rotation. 26 SYSTEMATOLOGY OF THE REGULAR FIGURES If P8T is an equilateral triangle, then the translation P~>T also belongs to the group.

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