sometimes with (several) equal sides,
two (opposite) right angles
comes in various forms
found in Cairo as paving tiles
(not that old)
what relationship is there between the angles if two are right angles and two of the other (obtuse) angles are equal?
what if the remaining 3 of them are equal?
so far the oldest dated version he has been able to establish is 1956
due to the two 90 degree angles in the pentagon
the tessellation(s) have a 'skeleton' (as David Wells calls them) of squares
so the variety of tessellations is created by the different angle in the rhombus:
or another way
are these squares?
what relationship is there for the apex and two equal base angles?
or with trapeziums
what is the relationship here?
a version of the tiling can be created from the 4, 3, 3, 4, 3 semi-regular tessellation (as a dual)
what are the angles in the tiles?
are the tiles congruent?
a tessellation of Cairo-like tiles can be drawn on isometric paper
but... there are two different types of pentagon here
establish that their angles are the same
David Bailey quotes Robert H Macmillan's claim that collinearity is a feature of some of the tessellations and explores this
what are the angles in each pentagon tile for this arrangement?
what collinearity is there?
all the sides the same length
what are the angles for this equilateral pentagon tile?
if the triangle formed by joining the apex of the pentagon to the two bottom corners is equilateral
there is a collinearity
find angle 'a'
and establish the (seeming) collinearity property