Double Tenth Day, 國慶日/雙十節 , National Day of Taiwan, celebrated by Honeycomb (10,10)

Greetings – today is 10/10/2015. here is the post I made for Taiwan last year.

Where to sit at the grand Gwangbokjeol   조국해방의 날 Dinner for delegates to the  Bridges 2014  Conference in Seoul? I was one of the last to descend the stairs to the conference centre floor and the tables were filling rapidly. I had met a Taiwanese couple while struggling to communicate with a Korean-speaking laptop; they caught my eye and beckoned me over to their table for what became a memorable evening. (See the Thank You to Bridges and Gwangbokjeol posts) As a belated thank you, here is a link to Bih-Yaw Jin’s  Torus Knots paper and a realisation of Honeycomb Lattice Labyrinth (10,10) in hounour of Taiwan’s National Day, Double Tenth Day, 國慶日/雙十節 , rendered in an approximation to the colours of the flag of Taiwan. Each supertile consists of 600 equilateral triangles and the way these are distibuted across six parallelogram about the axis of hexagonal symmetry generates a compelling three-dimensional effect.


Here is a guerilla tessellation of Liberty Square, Taipei employing the same Lattice Labyrinth design. A bit too brightly coloured, perhaps. And who can that be in the foreground?

tai squre2

Whoever they are,  they can be glimpsed again, approaching Taipei City Hall.


 What I see as a shrivelling of opportunities in the United Kingdom is leading to a diaspora of enterprising young Britons across the world.  Darren Booker, the brother of David, who manages Scarthin Books ,  runs a British-themed Fish and Chip restaurant and music venue in Taipei, so I’m sending my best wishes to Dazzler’s. I believe he’s about to open a  branch at the seaside.

Comments are welcomed at and the link How to do it  will take you to a source for the inexpensive Lattice Labyrinth Tessellations  workbook.


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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4 Responses to Double Tenth Day, 國慶日/雙十節 , National Day of Taiwan, celebrated by Honeycomb (10,10)

  1. ivasallay says:

    The Honeycomb Lattice Labyrinth (10,10) is so beautiful!

    Liked by 1 person

    • davescarthin says:

      Symmetry and intricacy seem to add up to beauty – family likenesses are strong within families and subfamilies of lattice labyrinths. I might manage to do a personal tessellation for ivasallay and for abyssbrain if you’d like to give me a significant date – privately via email if you like, to avoid identity theft (I’m reconciled to my own)

      Liked by 1 person

      • ivasallay says:

        Do you need just the month and the day, or is the year needed, too?


      • davescarthin says:

        Either the month and the day, which provides the number pair I hope it isn’t (31,12) OR your birthYEAR, which becomes the number of squares or triangles in each supertile, or, maybe in each fundamental domain ( sum of one supertile in each orientation). The latter condition means that the year has to be of the form a^2 + b^2 for square lattice tessellations or a^2 + ab + b^2 for triangular lattice tessellations OR a small multiple of these sums and not all years qualify – see early posts listing at least some possible years. Month and day give more manageable tessellations IF I can manage to find a construction.


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