Dodecahedral calendar with an Hamilton cycle which is twisting free

Here are calendars on a regular dodecahedron such that the twelve months form an Hamiltonian cycle. Furthermore, following the months from January to December and then back to January, you observe that January has the same orientation as you started. This demonstrates the result from the paper Hamiltonian cycles on Archimedean solids are twisting free in American Mathematical Monthly 121 (2014), 158--161.

The 2018 calendar in English.

The 2017 calendar in Dutch, English, French, German, Portuguese, Spanish and Swedish.

The 2016 calendar in English, French, German and Swedish.

The 2015 calendar in English, French, German and Swedish.

The 2014 calendar in English.

This calendar was obtained by downloading the Postscript file from The amazing twelve sided calendar site by Ole Arntzen and changing the Postscript file according to:

  1. Replace the line
    /mon [1 2 3 4 5 8 9 10 11 12 7 6] def % position -> logical month
    with
    /mon [1 2 3 4 12 9 8 5 6 7 10 11] def % position -> logical month
    This permutes the months into an Hamiltonian cycle.
  2. Replace the lines
    m 1 eq { /rot 3 def } if
    m 7 eq { /rot 2 def } if
    m 12 eq { /rot 1 def } if

    with the lines
    m 1 eq { /rot 1.5 def } if
    m 2 eq { /rot 4 def } if
    m 3 eq { /rot 3.5 def } if
    m 4 eq { /rot 3 def } if
    m 5 eq { /rot 0.5 def } if
    m 6 eq { /rot 0 def } if
    m 7 eq { /rot 1.5 def } if
    m 8 eq { /rot 2 def } if
    m 9 eq { /rot 2.5 def } if
    m 10 eq { /rot 0 def } if
    m 11 eq { /rot 0.5 def } if
    m 12 eq { /rot 1 def } if

    This rotates each of the months.

If you need the calendar with a different language, please download the postscript file from the calendar site in the right language and change the file as above.

A big thank you to Ole Arntzen for showing how to do this Postscript hack.


jrge@ms.uky.edu