Cutting a Hexagon

Geometry Level 3

Is it possible to cut a regular hexagon into pieces such that each piece is a regular polygon, but without cutting through any of the vertices of the original hexagon?

Inspiration

Yes No

Geoff Pilling by Geoff Pilling , 53, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Paul Hindess
Dec 8, 2016

Unlike Geoff, my solution resembled part of a semi regular 3-6-3-6 tiling (containing 7 regular hexagons and 12 equilateral triangles). Not sure how to post an image, so I hope the description suffices!

Edit: here's a quick pic:

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Pi Han Goh - 4 years, 6 months ago

Log in to reply

Thanks Pi. I don't think that button is available on the app, but I've seen it on the web version of Brilliant so looks like I'll be using my laptop in future. (-:

Paul Hindess - 4 years, 6 months ago

Nice! I posted follow up problem on what is the minimum number of regular polygons you can cut.

Geoff Pilling - 4 years, 6 months ago
Geoff Pilling
Dec 8, 2016

Yes \boxed{\text{Yes}} , like the big blue hexagon in this picture:

4 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...