Honeycomb Lattice Labyrinth (60,27) – The Irish Giant

Although the close relationship with Star Labyrinth(60,27) is clear (see the last post), Honeycomb (60,27) makes quite a different overall impression. A central hexagonally symmetrical supertile of the IRISH GIANT is shown, together with six fainter fellows, just to prove it really does tessellate. Each supertile is comprised of 11,898 equilateral triangles.

I haven’t counted them, but trust the value of the expression 2(602 + 60×27 + 272), the expression in the brackets is known as a Loeschian Number.

Here is the full GIANInteresting how the eye/brain does not just interpret the colours differently according to the colour of their neighbours but is beginning to meld the red and yellow into orange and the blue and red into purple.Honeycomb(60,27)Here, below, is just one of the supertiles of this Supergiant’s Causeway. Basalt never cooled like this.


About davescarthin

After terminating academic and local government careers, long an independent bookseller/publisher at Scarthin Books, Cromford, Derbyshire, UK. An antiquarian bookseller in two senses, I now have more time to be an annuated independent post-doc, developing the long dormant topic of lattice labyrinth tessellations - both a mathematical recreation and a source of compelling practical tiling and textile designs. Presenting a paper and experiencing so many others at Bridges Seoul 2014 Mathart conference was a great treat, as were the spirited MathsJam Annual Conferences in November 2016 and 2017. I'm building up to a more academic journal paper and trying hard to find practical outlets in graphic design and landscape architecture. I submitted 8 ft square tiling designs to the Wirksworth Festival Art and Architecture Trail in 2016 and 2017. I love giving illustrated talks, tailored to the audience. Get in touch to commission or to collaborate.
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