Euler and 6TET

When I walk from the university to my house, I sing improvisations in the
whole tone mode. Today I just realised that 6TET is an Euler genera.

Eu(0,2,2) or (5.5.7.7), Origin = 35 (0,1,1)

7Gb Bb 7D-

Ab+ C E-

LBb+ LD LF#-
*
/ \
/ \
/ 7D- \
/ \
*-------- E- -------*
/ \ / \ /
/ \ LF#-/ \ /
/ \ / 7Bb \ /
/ \ / \ /
*-------- C --------*
/ \ / \ /
/ \ LD / \ * /
/ * \ / 7Gb \ /
/ \ / \ /
*-------- Ab+ ------*
\ /
\ LBb+/
\ /
\ /
*

Unison vectors:
1/1 = 2/1 = (8/7)**6
8/7 = 9/8
5/4 = 9/7

Periodicity matrix using 2-3-5-7:
[ 1 0 0 0 ] Octave equivalence, C1 = C2
[ -4 -1 0 2 ] 64/63, D = 7D
[ 2 2 -1 -1 ] 36/35, LE = E-
[ -17 0 0 6 ] C = LLLLLLB#

Periodicity matrix using 5-7:
[ 3 0 ]
[ 1 2 ]

This is a twisted torus, similar to 12TET in 5-limit JI;

Periodicity matrix of 12TET using 3-5:
[ 12 0 ]
[ 4 -1 ]

-Kami