# Tessellation Symmetry: Rotation (Turning / Spinning)

### 1 2 3 4 5 6 7

This is the basic "tile" shape of the first goldfish tessellation on this page: it's a goldfish. We make this tessellation by copying the fish shape and then turning it a little around a point...in this case, where three fishies' back-fins meet.

The shape of the fish repeats by rotating...turning...spinning.

In the first example at right, the golfish turns 120 degrees, then does it again, to make three fish in each cluster. In other rotational tessellations, like the second example at left, a tile might turn 180 degrees, and do it only once.Those pairs of goldfish are turning around their tummies.

In other rotational tessellations the tile-- the basic repeating shape-- might rotate 90 degrees four times, and so on. Can you guess how many times a tile would rotate, if each turn were 60 degrees? 45 degrees? 30 degrees? 20 degrees? 15 degrees? Hint: 360 is an important number in geometry.

In the picture above, how many shells are clustered and rotated around each meeting-point?
How many degrees is each shell rotated, compared to the shell next to it?

This goldfish tiling uses rotational symmetry.
The golfish are turning 120 degrees twice.

In this version of the goldfish tiling,
the golfish are turning 180 degrees, just once.

See how these stingrays turn around a point, where three rays' noses meet.

These seahorses repeat and turn around a point where three chins meet, and also around a point where three tails meet.