4 papers
Cyclotomic points on varieties and all rational -monotiles
Jinjin Liang, Yixi Liao, Erxiao Wang
By computing all cyclotomic points on some algebraic varieties, we get an independent and efficient way to find all rational -monotiles for the sphere, thereby completing the…
Tilings of the sphere by congruent pentagons V: Edge combination with rational angles
Jinjin Liang, Yixi Liao, Wenchuan Hu +1
We classify edge-to-edge tilings of the sphere by congruent pentagons with the edge combination and with rational angles in degree: they are a one-parameter family of symmet…
Non-side-to-side tilings of the sphere by congruent triangles with any irrational angle
Wen Chen, Jinjin Liang, Erxiao Wang
We develop the basic and new tools for classifying non-side-to-side tilings of the sphere by congruent triangles. Then we prove that, if the triangle has any irrational angle in de…
Moduli Spaces of Pentagonal Subdivision Tilings
Jinjin Liang, Erxiao Wang, Min Yan
Pentagonal subdivision gives three families of edge-to-edge tilings of the sphere by congruent pentagons. Each family forms a two dimensional moduli. We describe the moduli in deta…