A simple Mathematica metagon definition.


metagon[n_:8]:=
Module[{ l={}, x=0, y=0, phi=0, i, j, k, dphi },
Do[dphi=2. Pi/i;
k=If[i==3, 1, If[i==n, 1, 2]];
Do[AppendTo[l, {-x, y}];
phi+=dphi; x+=Cos[phi]; y+=Sin[phi];
If[Abs[x]<0.0001, x=0]; If[Abs[y]<0.0001, y=0],
{j, 1, i-k}], {i, 3, n}]; l]


metagon[]

{{0, 0}, {0.5, 0.866025}, {1., 0}, {0.133975, -0.5}, {-0.366025, 0.366025},

> {0.303105, 1.10917}, {1.21665, 0.702434}, {1.11212, -0.292088},

> {0.198577, -0.698825}, {-0.61044, -0.11104}, {-0.505912, 0.883482},

> {0.407634, 1.29022}, {1.29522, 0.829576}, {1.48848, -0.151572},

> {0.841876, -0.914402}, {-0.157677, -0.884486}, {-0.757499, -0.0843526},

> {-0.615857, 0.905565}, {0.184277, 1.50539}, {1.17419, 1.36375},

> {1.77402, 0.563612}, {1.63237, -0.426306}, {0.832241, -1.02613}}