Equilateral Pentagons
That Tile The Plane
And Their Different Tilings

Livio Zucca

Tiling With Order 5 Rotational Simmetry

On this page we consider the equilateral pentagon only. If you want to see general pentagon tilings, go on this page, maintained by Ed Pegg Jr.

We want to consider all the equilateral pentagons that, for the particular values of their angles, tile the plane with different topology.

We defined five families of equilateral pentagons that tile the plane:


1) With two consecutive angles that their sum is equal to 180:

Consecutive angles sum = 180 Consecutive angles sum = 180 Consecutive angles sum = 180 Consecutive angles sum = 180


2) With two non-consecutive angles that their sum is equal to 180:

Non-consecutive angles sum = 180 Non-consecutive angles sum = 180 Non-consecutive angles sum = 180 Non-consecutive angles sum = 180 Non-consecutive angles sum = 180 Non-consecutive angles sum = 180 Non-consecutive angles sum = 180


3) With two consecutive angles that their sum is equal to 360:

Consecutive angles sum = 360 Consecutive angles sum = 360 Consecutive angles sum = 360 Consecutive angles sum = 360


4) With two non-consecutive angles that their sum is equal to 360:

Non-consecutive angles sum = 360 Non-consecutive angles sum = 360 Non-consecutive angles sum = 360 Non-consecutive angles sum = 360 Non-consecutive angles sum = 360 Non-consecutive angles sum = 360 Non-consecutive angles sum = 360 Non-consecutive angles sum = 360 Non-consecutive angles sum = 360 Non-consecutive angles sum = 360 Non-consecutive angles sum = 360


5) Without any of the previous characteristics:

Non complementary 180 or 360


Click each pentagon to see the relative tiling.

Notice: All the pink or green pentagons tile the plane also as the brown pentagon of their family. A pink or green pentagon tiles the plane with particular topology for the particular value of an other angle. The green pentagons are members of two family and they link an only web-page.



_________________

It isn't trivial!

First edition: Oct 20th, 2003 - Last revision: Oct 20th, 2003

Separator

Homepage of Livio Zucca livzucca@tin.it

Below you'll find a mirror of Livio Zucca pages. Click here for my home