A374948 - OEIS

A374948

Decimal expansion of the Euclidean length of the minimum Steiner tree joining all the vertices of a unit cube.

6, 1, 9, 6, 1, 5, 2, 4, 2, 2, 7, 0, 6, 6, 3, 1, 8, 8, 0, 5, 8, 2, 3, 3, 9, 0, 2, 4, 5, 1, 7, 6, 1, 7, 1, 0, 0, 8, 2, 8, 4, 1, 5, 7, 6, 1, 4, 3, 1, 1, 4, 1, 8, 8, 4, 1, 6, 7, 4, 2, 0, 9, 3, 8, 3, 5, 5, 7, 9, 9, 0, 5, 0, 7, 2, 6, 4, 0, 0, 1, 1, 1, 2, 4, 3, 4, 3

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OFFSET

1,1

COMMENTS

The 1994 Bridge's paper entitled "Minimal Steiner Trees for Three Dimensional Networks" (see Links) suggested an optimal strategy to solve the minimum Steiner tree problem for the unit cube {0,1}^3, and the total length of the provided Steiner Tree is 1 + 3*sqrt(3).

Also the surface area of a gyroelongated square pyramid (Johnson solid J_10) with unit edges. - Paolo Xausa, Aug 04 2025

LINKS

Table of n, a(n) for n=1..87.

Richard Bridges, Minimal Steiner Trees for Three Dimensional Networks, Math. Gaz., 78 (1994), 157-162.

Math Overflow, Joining the 2^k points of {0,1}^k with the shortest tree.

Mathematics Stack Exchange, Steiner tree problem in 3D.

J. MacGregor Smith, Rich Weiss, and Minoo Patel, An O(N2) Heuristic for Steiner Minimal Trees in E3, Networks 26 (1995), 273-289.

Badri Toppur and J. MacGregor Smith, A Sausage Heuristic for Steiner Minimal Trees in Three-Dimensional Euclidean Space, J. Math. Modelling and Algorithms, 4 (2005), 199-217.

Wikipedia, Gyroelongated square pyramid.

Index entries for algebraic numbers, degree 2.

FORMULA

Equals 3*sqrt(3) + 1.