Yixi Liao

activity

20212026

most citedTilings of the sphere by congruent quadrilaterals II: edge combination

a^{3} b

with rational angles

2 citations · 2 across the 6 of their papers we have counts for

collaborators

7 papers

math.MG2026

Area and diameter gaps for hyperbolic monotiles

Yixi Liao, Erxiao Wang

For each fixed $n$ , we prove a positive lower bound for the diameter of a compact simple geodesic $n$ -gonal monotile of the hyperbolic plane. We also prove a positive lower bound f…

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…

math.CO2022

Tilings of the sphere by congruent quadrilaterals III: edge combination $a^{3} b$ with general angles

Yixi Liao, Pinren Qian, Erxiao Wang +1

Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This last one classifies the case of $a^{3} b$ -quadrilaterals wit…

math.CO2022★ 2 cited

Tilings of the sphere by congruent quadrilaterals II: edge combination $a^{3} b$ with rational angles

Yixi Liao, Erxiao Wang

Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Dio…

math.CO2021

Tilings of the sphere by congruent quadrilaterals I: edge combination $a^{2} b c$

Yixi Liao, Pinren Qian, Erxiao Wang +1

The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^{2} b c$ are classified as $3$ classes: a sequence of two-parameter families of $2$ -layer earth map tiling…

Area and diameter gaps for hyperbolic monotiles

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

Tilings of the sphere by congruent quadrilaterals III: edge combination a3b with general angles

Tilings of the sphere by congruent quadrilaterals II: edge combination a3b with rational angles