## Schaad's 7-fold

### Info

Schaad’s 7-fold is a variation of Madison’s 7-Fold,
hence it shares many properties with it.
It allows for tilings with global 7-fold symmetry and a lot of locally 7-fold symmetric patches.
There are three tile shapes, but only seven instead of nine different
prototiles. The inflation factor is a
PV number:
`$2+2\cos\left(\frac{\pi}{7}\right)+2\cos\left(\frac{2\pi}{7}\right) = 5.04891733952231\ldots$`

which is the largest root of `$x^{3}-6x^{2}+5x-1$`

.

### Substitution Rule

### Patch

download vectorformat Schaad's 7-fold

### References

[ss2022]

P. Stampfli and T. P. Schaad

**Ptolemy, the Regular Heptagon, and Quasiperiodic Tilings**

*Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture*
2022,
39,
135-142,
bridges2022-135.pdf