Spherical

In this geometry, any pair of non-antipodal points can be connected with a unique line segment; this is not the case for antipodal points like the N and S poles (Euclid's Postulate 1). Straight lines can still be extended indefinitely (Postulate 2). However, this does not mean that they are infinitely long, as Euclid probably intended: they eventually wrap back atop themselves. In addition, there are no such things as parallel lines in spherical geometry (Postulate 5).

Constructions Included:

06-hedron:

04-hedron:

inCircle:

inExCircles:

circumCircle:

12-hedron:

earth:

08-hedron:

quadMPquad:

PolTriTheorem:

20-hedron:

diameterTriangle:

rightTriangle: