board 2
board 2
Back to Geometry
The Impossible Machine
Crosses
Although crosses have gained a kind of ungainly significance
in relation to Christianity, it seems useless to me to regard
them any differently than other mathematical line
constructions, since they form the natural link between the
unity of circle, and the composition of polygons, which
necessarily involve more than two lines. Notice how since by
definition crosses are not defining any volumetric space,
crosses progress by the number of crossing points rather
than the number of lines.
CROSS 0

Value 2 (2 Lines)
1 Crossing point

Transforms to Cross 1 or Star 0



CROSS 1

Value 3 (3 Lines)
2 Crossing points

Transforms to Cross 2 or reverses to
Cross 0



CROSS 2

Value 3 (3 Lines)
3 Crossing points

Transforms to Cross 3 or reverses to
Cross 2



CROSS 3

Value 4 (4 Lines)
4 Crossing points

Transforms to Cross 4 or reverses to
Cross 2



CROSS 4

Value 5 (5 Lines)
At least 5 Crossing points

Transforms to Cross 5 or reverses to
Cross 3




CROSS 5

Value 6 (6 Lines)
At least 6 Crossing points

Transforms to Cross 6 or reverses to
Cross 4
cross
cross 0
cross 1
cross 2
cross 3
cross 4
cross 5
Meta Crosses
META CROSSES
Open and Closed Crosses
OPEN AND
CLOSED
CROSSES AS
GRAPHIC LOGIC