SPECIAL CLASSES
OF
LUNDADESIGNS
Figure 16.
Especially attractive are Lundadesigns which display extra symmetries.
Figure 16 presents the six possible 3x3 Lundadesigns
(being white
(= 0)
the colour of the first unit square with
vertices (0,0), (1,0), (1,1), and (0,1)), which admit
reflections in the diagonals that preserve
the colours and vertical and horizontal reflections
interchanging black and white. By consequence, a halfturn
about the centre preserves the colours and a quarterturn
reverses the colours. Abreviately, these finite designs
are of the type d4'
(for this notation, see e.g. Washburn & Crowe, p. 68).
Figure 17.
Figure 18.
Figure 19.
Figure 17 displays the 18 4x4 Lundadesigns and
Figure 18 the 84 5x5 Lundadesigns which have the same symmetries.
Figure 19 presents examples of mirror designs which generate
such 5x5 Lundadesigns (the numbers indicate the corresponding
Lundadesigns in Figure 18).
Figure 20.
When we join four Lundadesigns of the type d4',
a new Lundadesign of the same type is obtained (see the example in Figure 20).
Figure 21.
Figure 21 displays examples of 5x5 Lundadesigns 
together with corresponding generating mirror designs, which,
although they do not have symmetry axes, do possess the property
that a quarterturn about the respective centre reverses the colours,
and consequently a halfturn preserves the colours (type c4').
Figure 22.
Figure 23.
Figure 24.
Figure 25.
Figure 26.
Figure 22 presents examples of 9x9 Lundadesigns of
the type d4' together with corresponding
generating mirror designs. Figure 23 does the same for
7x7 Lundadesigns of the type c4'.
Examples of 9x9 and 13x13 Lundadesigns of the same type
c4' are displayed in Figures 24 and
25.
Two examples of 9x9 Lundadesigns which admit reflections in
their diagonals are given in Figure 26.
