Yixi Liao

collaborators

3 papers

math.CO2025

Cyclotomic points on varieties and all rational $a^{3} b$ -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 $a^{3} b$ -monotiles for the sphere, thereby completing the…

math.CO2025

Tilings of the sphere by congruent pentagons V: Edge combination $a^{4} b$ 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 $a^{4} b$ and with rational angles in degree: they are a one-parameter family of symmet…

math.CO2024

Tilings of the sphere by congruent pentagons IV: Edge combination $a^{4} b$ 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 $a^{4} b$ and with any irrational angle in degree: they are three $1$ -parameter familie…

Cyclotomic points on varieties and all rational a3b-monotiles

Tilings of the sphere by congruent pentagons V: Edge combination a4b with rational angles

Tilings of the sphere by congruent pentagons IV: Edge combination a4b with general angles

Cyclotomic points on varieties and all rational $a^{3} b$ -monotiles

Tilings of the sphere by congruent pentagons V: Edge combination $a^{4} b$ with rational angles

Tilings of the sphere by congruent pentagons IV: Edge combination $a^{4} b$ with general angles