5 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…
Tilings of the sphere by congruent pentagons IV: Edge combination with general angles
Junjie Shu, Yixi Liao, Erxiao Wang
We classify edge-to-edge tilings of the sphere by congruent pentagons with the edge combination and with any irrational angle in degree: they are three -parameter familie…
Tilings of the sphere by congruent regular triangles and congruent rhombi
Qi Yuan, Erxiao Wang
All edge-to-edge tilings of the sphere by congruent regular triangles and congruent rhombi are classified as: (1) a -parameter family of protosets each admitting a unique $(2a^3…