Hendecagonal Meteorite

Hendecagonal Meteorite

29 March, 2023

11-Colouring

110011006031111081105

n-colouring 110011006031111081105

Loop Cycles

\(2\mathord*(t_1-,f2)\;\)\(2\mathord*(t_2-,f1)\;\)\(2\mathord*(t_3)\;\)\(2\mathord*(t_3-,f2)\;\)\(5\mathord*(t_4)\;\)

Gyre Multipliers

\(-\)

Growth

Loop(s) Boundary Vertices

Topology Type

Finite Genus

Skeleton Type

Unknown

Files

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Embedding

Notes

Hard to count the holes in this hendecagonal tiling of a genus 1651 surface. A nice embedding, making the 3960 tiles and the structure more visually readable, seems unattainable. More meteor than anything else.

Dual Group

\(G_d=\)\(\left\langle \: S_d \:\middle|\:R_d\:\right\rangle\)
\(S_d=\)\({f_1},\:\)\({f_2},\:\)\({f_3},\:\)\({t_1},\:\)\({t_2},\:\)\({t_3},\:\)\({t_4}\)
\(R_d=\)\({f_1}^2,\:\)\({f_2}^2,\:\)\({f_3}^2,\:\)\({t_1}^3,\:\)\({t_2}^3,\:\)\({t_1}{t_3}{t_2},\:\)\({t_4}^{-1}{f_2}{f_1},\:\)\({t_4}^{-1}{f_3}{t_3},\:\)\({t_3}^2,\:\)\({t_4}^5,\:\)\(({t_1}{f_2})^2,\:\)\(({t_2}{f_1})^2,\:\)\(({t_3}^{-1}{f_2})^2\)
\(|G_d|=\)\(3960\)

Vertex Group

\(G_v=\)\(\left\langle \: S_v \:\middle|\:R_v\:\right\rangle\)
\(S_v=\)\(a,\:\)\(b,\:\)\(c\)
\(R_v=\)\(a^2,\:\)\(b^3,\:\)\(c^3,\:\)\((ab^{-1})^2,\:\)\((bc^{-1})^2,\:\)\(ac^{-1}(ac)^2ab^{-1}c(ac^{-1})^2acac^{-1}b\)
\(|G_v|=\)\(3960\)