7 papers
Area and diameter gaps for hyperbolic monotiles
Yixi Liao, Erxiao Wang
For each fixed , we prove a positive lower bound for the diameter of a compact simple geodesic -gonal monotile of the hyperbolic plane. We also prove a positive lower bound f…
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…
Graded strength of comparative illusions is explained by Bayesian inference
Yuhan Zhang, Erxiao Wang, Cory Shain
Like visual processing, language processing is susceptible to illusions in which people systematically misperceive stimuli. In one such case--the comparative illusion (CI), e.g., M…
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…