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178 R. P. Mondaini and N. V. OliveiraBy forming a Steiner tree with points P j and S k with a 3-Sausage’s topology [4], we canobtain from the condition of edges intersecting at 120 ◦ , an expression for the radius functionr(ω, α) or:αωr(ω, α) = √ (4)A1 (1 + A 1 )whereA 1 = 1 − 2 cos ω. (5)The restriction to full Steiner trees can be obtained from eq. (1) alone. We then have for theangle of consecutive edges formed by the given points− 1 2 ≤ cos θ(ω, α) = −1 + (1 + A 1 ) 22(α 2 ω 2 + 1 + A 1 ) . (6)2. The generalization of the formulae to sequences ofnon-consecutive pointsThe generalization of the formulae derived in section 1 to non-consecutive points [5] alonga right circular helix is done by taking into consideration the possibility of skipping pointssystematically to define subsequences. Let us consider the subsequences of fixed and Steinerpoints respectively.(P j ) m, ljmax: P j , P j+m , P j+2m , ..., P j+ljmax . m(7)(S k ) m, l k max: S k , S k+m , S k+2m , ..., S k+l k max . m (8)with 0 ≤ j ≤ m − 1 ≤ n − 1, 0 ≤ k ≤ m − 1 ≤ n − 2 and[ ] [ ]n − j − 1n − k − 2lmax j =; lmax k =mm(9)where (m − 1) is the number of skipped points and the square brackets stand for the greatestinteger value. It is worth to say that the sequences (1) and (3) correspond to (P 0 ) 1,n−1 and(S 1 ) 1,n−2 respectively.The n points of the helical point set are then grouped into m subsequences and we considera new sequence of n given points which is written asP j =m−1⋃j=0(P j ) m, ljmax(10)Analogously, a new sequence for the union of the subsequences of the Steiner points isintroduced in the formS k =m−1⋃k=1(S k ) m, l k max(11)If the points P j+lm , S k+lm are evenly spaced along the helices, their coordinates are givenanalogously to eqs. (1) and (3) of section 1. We can write,P j+lm (cos(j + lm)ω, sin(j + lm)ω, α(j + lm)ω) (12)S k+lm (r m (ω, α) cos(k + lm)ω, r m (ω, α) sin(k + lm)ω, α(k + lm)ω) . (13)