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The Aperiodical’s Actually Hexagonal Snowflake Competition 2015

no bad snowflakes


To celebrate the year end, as well as our daily Advent Calendar posts, we’re also running a little competition – last year we did a pun competition, and this year it’s something a bit more crafty – well, it’s a knitting competition in which the knitting is optional.

Matt Parker’s annual campaign against non-hexagonal snowflake symmetry continues apace, and this year he’s even spotted a knitted Christmas jumper with octagonal offenders:

Admittedly, the design in Matt’s tweet above is actually a Nordic rose, and therefore not really meant to be a snowflake – but it’s coloured like one, and plenty of knitted atrocities exist – check the #snowfake hashtag for examples. Anyway, a small discussion follows about whether it is indeed even possible to use knitting (conventionally stitches are arranged in a square grid) to produce a convincing hexagonal snowflake, and we thought we’d settle the debate, so we’re launching…

The Aperiodical’s Actually Hexagonal Snowflake Competition 2015

The rules are as follows:

Your entry must consist of a design for a snowflake, which should have hexagonal ($\mathrm{Dih}_6$) symmetry, and consist of a pattern which could be knitted in a square grid of stitches. Two or more colours may be used. Entries can be in two categories:

1: Actual Knitted Actual Hexagon

If you’re skilled enough to actually knit your design into a piece of knitting, we’d love to see it – we’d like to see a photo from during the knitting process, and one of the finished item (since we’d like proof you actually knitted it).

2: Pixel Design only

If you’re not a knitter, your entry can also come in the form of an image/spreadsheet showing your proposed layout of pixels, clearly indicating the arrangement of pixels and colours.

Entries for both categories should be reasonably small – the whole design should fit in a square 36 pixels/stitches across. We’ll be judging the entries on how symmetrical they are and how snowflakey they look, and if you can incorporate amusing mathematical shapes/symbols too without breaking the symmetry, that won’t count against you.

Please send your answers by email (with photos/designs attached) to by the end of 31st December 19th January (we’ve extended the deadline, since people have been busy over Christmas and we’d love to get more entries) – we’ll pick our favourites and announce the winners shortly after that.

We have two exciting prizes:


The winner of the knitted category will receive a deck of Math Stack playing cards (right), whose Kickstarter we posted about back in June, and which are now available to buy from Maths Gear.

91Hp0TVSyjL._SL1500_The winner of the design category will receive an actual knitted item incorporating their snowflake design, knitted by one of our expert team of mathematical knitters, plus a copy of mathematical board game Fiendish Numbers.

Good luck – and watch out for those no-good #snowfakes!

5 Responses to “The Aperiodical’s Actually Hexagonal Snowflake Competition 2015”

  1. Avatar Pat Ashforth

    Most knitting stitches are not square. The ratio of stitches to rows, in the most widely used stitches, is around 7:10. Is it OK to have a width of 36 stitches and enough rows for the snowflake to appear ‘square’?

    Garter stitch does create square stitches so there are still ways that ‘pixel designs’ can be reproduced in knitting.

    • Avatar Madeleine

      Just scrolled down to point out that stitches aren’t square in stocking stitch but I see I’ve been beaten to it. This and the size limit will make for a tricky design challenge!

      • Avatar Denise

        In my (very limited) experience, stranded colorwork (as seen in the offending pullover), tends to draw the stitches in, so they more closely approximate squares. The Nordic rose as seen above at an angle looks like it might fit fairly neatly into a square.

        I suspect that “Two or more colours may be used.” probably should be read as “At least two colours must be used.”

        Fascinating challenge.

        • Avatar Katie

          Yes! I’m hoping all the designs will use at least two colours, but more is permitted. We’ve had some interesting entries already!

          I’m aware knitting stitches aren’t quite square, but to keep things simple (and so as not to confuse the non-knitters :P) we’ll assume they are, and judge the non-knitted entries as such. If you want to design a knitted entry with the stitch size ratio taken into account, please do – any reasonable bending of the rules will be tolerated in the spirit of the season.

  2. Avatar Doris

    What about knitting in the round? Seems as though you could cast on six stitches, and do paired increases at each of those six points. It would have to turn out six-pointed, either a hexagon (no decreases in between) or s six-pointed star (if you put decreases mid-way between the increases.

    Clearly, this does not meet your rules, but I think it would produce hexagonal symmetry in knitting.


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