A p4g tile -- p4'mg' if one focuses on the brown and yellow 'bow ties' --
manufactured by CEARCO (?) that I purchased from a kitchen
equipment store in the old town of Barcelona on November 24, 2001: that
city's streets are full of life and its stores are beautifully set up ...
so much so that I did walk unsuspectingly into the said store and found a
few copies of this tile piled up on a marginal shelf ... on my way out!
I had not seen this brilliant design before, not even in Syed Jan
Abas & Amer Shaker Salman's comprehensive "Symmetries of Islamic
Geometrical Patterns", until Hollister (Hop)
David directed me to page 27 of J. Bourgoin's classic "Arabic Geometrical
Pattern & Design": there the Barcelona tile stands silent and colorless!
Observe by the way that ... out of each 6-star's six
reflection axes, there exist precisely two that act as reflection axes for
the entire pattern ... and out of each hexagon's six reflection axes there
exists precisely one that acts, likewise, as a reflection axis for the
entire pattern: what else can I say?
[Well, I can add something here... Keeping only the hexagons and coloring
them blue and red led to two rather challenging final exam patterns: a
p4'mg' on 5/14/02 and a Pc'4 on 5/16/02; although my students had inevitably
seen the Barcelona tile, most of them couldn't see the connection between
it and problem 6f on their test ... and those fourfold centers in particular!]