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# Can you pave the plane with identical tiles?

Published on Jul 19, 2019198 Views

Everybody knows that identical regular triangles or squares can tile the whole plane. Many people know that identical regular hexagons can tile the plane properly as well. In fact, even the bees know

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#### Chapter list

Can You Pave the Plane with Identical Tiles?00:00

What kind of polygons can tile the whole plane?00:33

Tiling is one of the ancient subjects in mathematics00:51

Convex Bodies and Lattices02:28

Lattice03:32

Lattice Tilings, Fedorov's Discovery04:42

Theorem 106:46

Hilbert's Problem and Bieberbach's Question08:07

Problem 109:53

Classifcation of the Two-dimensional Tiles11:20

Theorem 212:41

Theorem 3 - 114:32

Remark16:17

Theorem 3 - 221:33

Theorem 3 - 322:11

Theorem 422:29

Multiple Tilings23:03

Problem 225:49

Multiple Lattice Tilings31:41

Example 133:46

Theorem 535:41

Theorem 6 - 138:33

Theorem 6 - 239:07

Multiple Translative Tilings - 141:42

Multiple Translative Tilings - 242:56

Multiple Translative Tilings - 344:24

Theorem 746:10

Theorem 8 - 147:22

Theorem 8 - 248:19

References48:23