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sidedifferent

Sidedifferent is a roughly informal mathematical term used to describe a polygon in which no two sides have the same length. It is not standard terminology, and many texts refer to the same idea via scalene or irregular polygons. In triangles, a sidedifferent triangle is what most would call a scalene triangle: all three side lengths are different. For polygons with four or more sides, a polygon with pairwise unequal side lengths is sometimes called a sidedifferent polygon, though the more common label is simply a scalene polygon, or an irregular polygon when angle measures vary.

The main characteristic is the absence of equal-length sides. This generally implies minimal or no symmetry;

Construction and existence: To form a simple polygon with specified distinct side lengths, a necessary condition

Relationship to symmetry and angles: No requirement on interior angles; some may be acute, obtuse, or right,

See also: Scalene polygon; Irregular polygon.

in
practice
a
sidedifferent
n-gon
has
only
the
trivial
symmetry
(the
identity)
unless
other
geometric
coincidences
occur.
is
that
the
longest
side
be
shorter
than
the
sum
of
the
remaining
sides
(polygon
inequality).
Beyond
this,
arranging
the
sides
and
angles
to
close
the
figure
requires
appropriate
turning
angles,
which
is
always
possible
in
many
cases.
as
long
as
all
sides
differ.
The
property
concerns
side
lengths,
not
angle
measures.