Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
A huge wheel is rolling past your window. What do you see?
Is it true that any convex hexagon will tessellate if it has a pair
of opposite sides that are equal, and three adjacent angles that
add up to 360 degrees?
A design is repeated endlessly along a line - rather like a stream
of paper coming off a roll. Make a strip that matches itself after
rotation, or after reflection
When a strip has vertical symmetry there always seems to be a
second place where a mirror line could go. Perhaps you can find a
design that has only one mirror line across it. Or, if you thought
that. . . .
I noticed this about streamers that have rotation symmetry : if
there was one centre of rotation there always seems to be a second
centre that also worked. Can you find a design that has only. . . .
Look at this cunning detective work which helped to unravel the mystery.
Go to last month's problems to see more solutions.
Toni Beardon has chosen this article introducing a rich area for
practical exploration and discovery in 3D geometry
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
A Sudoku that uses transformations as supporting clues.