C  =  circle made by intersection of the xy-plane and unit sphere S

CO  =  (0,0,0)  =  origin =  center of circle C

r = $\sqrt{1-{s_z}^2}$  =  radius of circle C

(r,0,0)  =  intersection of positive x-axis with unit sphere S  =  SN (north pole)
(-r,0,0)  =  intersection of negative x-axis with unit sphere S
(0,r,0)  =  intersection of positive y-axis with unit sphere S
(0,-r,0)  =  intersection of negative y-axis with unit sphere S

z  =  length from origin to center of unit sphere

S  =  unit sphere

S =  (0,0, sz )  =  center of unit sphere S, where -1 < sz < 1

SN  =  (r,0,0)  =  north pole of unit sphere S

SC  =  (0,0,1-z)  =  projection of line segment between SO and CO to the surface of sphere S

N  =  cone having circle C as its base and sphere center SO as its apex

P =  (r cos $\phi$, r sin $\phi$,0)  =  tangent point on circle C where planes $\mathbb{B}$, $\mathbb{G}$, and $\mathbb{Y}$ intersect

h  =  arc length of circle C from P to SN
h  = ${2r}\sin\frac{\phi}{2}$   (from analyzing a chord in circle C)
h  = ${2}\sin\frac{\lambda}{2}$   (from analyzing isosceles triangle ∆SNSOP, which has two sides  of length 1) $\mathbb{T}$ =  plane containing point SO and also the equator of sphere S $\mathbb{M}$ =  plane containing point SO and also the tangent (in the xy-plane) to circle C at point SN $\mathbb{B}$ =  plane containing point SO and also the tangent (in the xy-plane) to circle C at point P $\mathbb{G}$ =  plane containing point SO and point P and point SN $\mathbb{Y}$ =  plane containing point SO and point P and plane $\mathbb{Y}$ is perpendicular to plane $\mathbb{G}$

a  =  great circle arc λ
b  =  great circle arc υ
c  =  great circle arc ∠SCSOP

D =  midpoint of side a $\alpha$ =  ∠ $\mathbb{BG}$ $\phi$ =  arc length in degrees from (r,0,0) to point P   =   ∠SNCOP  =  dihedral ∠SN-SOCO-P $\lambda$ =  ∠PSOSN $\upsilon$  =  angle between the axis of cone N and the cardinal axis of sphere S  =   ∠SNSOCO.