A014529: Examples of polygons of maximum area made from n equilateral
triangles with sides s_k such that gcd(s_1,s_2,...,s_k)=1.

Converted from illustration in

Ian Stewart, Die unscheinbare Schwester der goldenen Zahl,
Spektrum der Wissenschaft, Dossier 02/2003:
Mathematische Unterhaltungen II, 55-57.

Hugo Pfoertner, 2017-08-17

Areas are given relative to the size of a triangle with sides=1.

 a(1) = 1
    *
   / \
  *---*


  a(2) = 2
    *---*
   / \ /
  *---*


  a(3) = 3
    *---*
   / \ / \
  *---*---*


  a(4) = 7
    *---*
   / \ / \
  *---*---*
   \     /
    +   +
     \ /
      *

  a(5) = 11
    *---*
   / \ / \
  *---*---*
   \     / \
    +   +   +
     \ /     \
      *---+---*

  a(6) = 20
    *---*---+---+---*
   / \ / \         /
  *---*---*       +
   \     / \     /
    +   +   +   +
     \ /     \ /
      *---+---*


  a(7) = 36
            *
           / \
          +   +
         /     \
        +       +
       /         \
      +           +
     /             \
    *---*---+---+---*
   / \ / \         /
  *---*---*       +
   \     / \     /
    +   +   +   +
     \ /     \ /
      *---+---*


  a(8) = 71
          *---+---*
         / \     / \
        +   +   +   +
       /     \ /     \
      +       *---+---*
     /         \     / \
    +           +   +   +
   /             \ /     \
  *---+---+---+---*       +
   \             /         \
    +           *---+---+---*
     \         / \         /
      +       +   +       +
       \     /     \     /
        +   +       +   +
         \ /         \ /
          *---+---+---*


  a(9) = 146
        *---+---+---*---+---+---+---*
       / \         / \             / \
      +   +       +   +           +   +
     /     \     /     \         /     \
    +       +   +       +       +       +
   /         \ /         \     /         \
  *---+---+---*---+---+---*   +           +
   \                     / \ /             \
    +                   *---*---+---+---+---*
     \                 / \                 /
      +               +   +               +
       \             /     \             /
        +           +       +           +
         \         /         \         /
          +       +           +       +
           \     /             \     /
            +   +               +   +
             \ /                 \ /
              *---+---+---+---+---*


  a(10) = 260
                  *---+---+---+---*
                 / \             / \
                +   +           +   +
               /     \         /     \
              +       +       +       +
             /         \     /         \
            +           +   +           +
           /             \ /             \
          +               *---+---+---+---*
         /                 \             / \
        +                   +           +   +
       /                     \         /     \
      +                       +       +       +
     /                         \     /         \
    +                           +   +           +
   /                             \ /             \
  *---+---+---+---+---+---+---*---*               +
   \                         / \ /                 \
    +                       *---*---+---+---+---+---*
     \                     / \                     /
      +                   +   +                   +
       \                 /     \                 /
        +               +       +               +
         \             /         \             /
          +           +           +           +
           \         /             \         /
            +       +               +       +
             \     /                 \     /
              +   +                   +   +
               \ /                     \ /
                *---+---+---+---+---+---*


  a(11) = 495
                          *---+---+---+---+---+---+---+---*
                         / \                             / \
                        +   +                           +   +
                       /     \                         /     \
                      +       +                       +       +
                     /         \                     /         \
                    +           +                   +           +
                   /             \                 /             \
                  +               +               +               +
                 /                 \             /                 \
                *---+---+---+---+---*           +                   +
               / \                 / \         /                     \
              +   +               +   +       +                       +
             /     \             /     \     /                         \
            +       +           +       +   +                           +
           /         \         /         \ /                             \
          +           +       *---+---+---*---+---+---+---+---+---+---+---*
         /             \     / \                                         /
        +               +   +   +                                       +
       /                 \ /     \                                     /
      +                   *---+---*                                   +
     /                     \     / \                                 /
    +                       +   +   +                               +
   /                         \ /     \                             /
  *---+---+---+---+---+---+---*       +                           +
   \                         /         \                         /
    +                       +           +                       +
     \                     /             \                     /
      +                   +               +                   +
       \                 /                 \                 /
        +               +                   +               +
         \             /                     \             /
          +           +                       +           +
           \         /                         \         /
            +       +                           +       +
             \     /                             \     /
              +   +                               +   +
               \ /                                 \ /
                *---+---+---+---+---+---+---+---+---*