Can a "biangle" on a sphere be considered a "regular polygon" on the sphere? I am being asked whether a lune on a sphere —that is, where the sphere is divided into four regions by the intersection of two great circles— can be considered a regular polygon on the sphere. Here, a regular polygon is defined as having all of its sides the same length and all of its angles the same measure.
My reasoning is yes, but wondering if it matters that these lines making up the polygon are all curved and that only congruent angles are considered to have the same measure.
 A: TL;DR: Yes, but...
Discussion:  First off, in terms of language usage, the region on the surface of a sphere bounded by two great-circle arcs is generally called a lune.  The terms digon and biangle are also used.  According to Googles Ngram viewer, the term "lune" is far-and-away the most common term, though this term has a few other uses in English which may confuse the issue a bit.  The terms "digon" and "biangle" are far less commonly used, and are used at roughly the same rate.
A spherical polygon is, roughly speaking, a region on the surface of a sphere which is bounded by great-circle arcs.  Note that, in the context of spherical geometry, a great circle is a straight line, and is not curved.  It only looks curved because the underlying space is curved.[1]  Per this definition, a lune is a spherical polygon.
A regular spherical polygon is a spherical polygon which is both equiangular (every pair of adjacent sides meet at an angle of the same measure) and equilateral (ever side has the same length).  Per this definition, every lune must be regular, as both sides of a lune are half the length of a great circle, and both angles have the same measure.
Finally, addressing the "but..." at the top, it is should be noted that referring to a lune as a "polygon" is imprecise.  It is not a polygon with respect to the usual definitions, which assume that space is Euclidean, rather than spherical (or hyperbolic).  More precisely, a lune is a regular spherical polygon.  Context will typically make this clear, but it can't hurt to be explicit.

[1]  By way of analogy, light moves along straight lines through a vacuum.  However, the path of a photon can be "bent" by a massive object, such as a black hole.  This is because such massive objects bend space itself.  The photon goes in a straight line through a warped space.
A: Yes it is a regular polygon. However, usually they are called digons and not biangles.
