Pentagonal Twisted 120-Cell Wrapping

7200 Pentagonal prototiles twist around the 120-cell skeleton. Take a walk on the petrie path and you will be back where you started after 150 alternating turns to the “left” and the “right” no matter where you take off and which way you go.

The twisted 120-cell wrap can be decomposed into sub-tilings with equally colored boundaries to get 1200 tubes along the edges of the 120-cell, 600 sub-tilegraphs wrapping the vertices or incredibly 5 sub-tilegraphs of 1440 tiles.

Naturally the tilegraph is of genus 601. It has 7200 automorphisms and the group $G$ acting on the tiles can be presented in the following way $G=\langle f_1,t_1,t_2\mid {f_1}^2,{t_1}^3,{t_2}^3,(t_1t_2)^2,(t_2f_1)^2,(t_1t_2f_1)^5\rangle$