Celebrating 5 years of DressCode Shirts with more geek style!

Today is our 5th birthday!

But it’s not really about us, it’s about you our customers, we have to say a really big "thank you" to everyone who has supported us, it really does mean a lot to have you with us.


Pentagon cake


What should we do to mark 5 years? The number really got us thinking and we soon fell down, way down the rabbit hole of the Pentagon and Pentagrams. Where there is geekery a plenty…


What is a Pentagon?

The word "pentagon" originates from two Greek words "pente" (five) and "gonia" (angle). The ancient Greeks were fascinated by the geometric properties of pentagons and spent a great deal of time exploring their mathematical significance, expressing these ideas through many different media and objects.

Regular Pentagon drawing

1) All 5 sides are equal

2) All inside angles are equal, 108 degrees

3) The sum of the interior angels is 540 degrees

4) All 5 exterior angles are equal, 72 degrees

5) The shape has 5 diagonals


Did you know, there's more than one Pentagon?

Not wanting to freak you out, but did you know there’s more than one kind of Pentagon? The ones that come front of mind are ‘regular pentagons’ or ‘equilateral pentagons’. To make things even more confusing, there are 3 methods by which these are created.

Richmond Method
Uses Pythagoras’ theory and is brilliantly explained in all it’s mathematical detail here.

Carlyle Circles
These pentagons are based around quadratic equation, using the radius of a circle to divide the shape up. Details here

Carlyle circles pentagon construction

Euclid’s Method
For a regular pentagon is also constructed using a compass and ruler, either by inscribing one within a circle or constructing one on a given edge of a circle.

Euclid method for forming a Pentagon

If, like me, your heads starting to hurt, just wait because the Pentagon is also something of a shape shifter, in that it can be both symmetrical and non symmetrical. And very beautiful.

Pentagon patterns

I think we are all agreed the Pentagon is a rather cool, geeky shape, created in a number of ways, and some of the Pentagons are not what we might typically think of as pentagonal. But this is also confusing. Then, the maths and confusion jump to another level, pentagonal tiling and patterns.


Pentagon patterns


The symmetrical shape cannot be tiled without the support of other shapes or the use of none symmetrical pentagons. It has been studied a lot, and one of the most recent papers is by Michaël Rao at Laboratoire d'informatique du parallélisme – who knew such a place existed? And let's be honest, because it's French, it sounds even more impressive.

Using computer assisted (AI) tools Rao was able to demonstrate that there are ONLY 15 five-sided patterns that can tile the plane.

Our minds are blown!

15 types of pentagons had been discovered between 1918 to 2015 as part of a research programme initiated by Karl Reinhardt in 1918. The programme went through a number of twists and turns, with new discoveries being made by amateur mathematicians as well as scientific groups.


15 type of pentagon


Then in 2015 a new 15th form of pentagon was confirmed, 30 years after the 14th one had been discovered! But the scientific community (in 2015) was still unable to determine whether there were other forms of pentagons that could tile the plane.

Pentagon tesselations

Enter Michael Rao in 2017, who was able to settle this very important problem, one that had been bothering scientists and mathematicians for over 100 years -not that they’d openly admit that of course. Rao’s methodology was open to new perspectives and ta dah - 15 Pentagons, all of which can tile the plane periodically (a scientific way of saying that the tiles repeat infinitely). There’s no denying the beauty of each and every one.


DressCode Aqua Pentagon pattern

Party on

This is the end of our first blog about pentagons to mark 5 years of DressCode Shirts, for some unfathomable reason, there will be another 2 posts, because doing 5 was just too much work!


AI generated pentagon pattern


If you like this sort of stuff, please share it with your friends who are equally passionate about it. And if you really want to 'Geek Out', there's a Pentagonal pattern shirt, along with several other Geek Chic designs available exclusively from DressCode.