also see Defining Geometric Figures
Ellipsoid
A threedimensional figure all planar
crosssections of which are either
ellipses or circles. 
Semiaxes: a, b, c (the semiaxis is
half the length of the axis, and
corresponds to the radius of a sphere)
Volume: V
V = (4 Pi/3)abc 


Prolate Spheroid
Semiaxes: a, b, b (a > b)
Surface area: S
S = 2 Pi b(b+a arcsin[e]/e),
where e = sqrt(a^{2}b^{2})/a

Oblate Spheroid
Semiaxes: a, b, b (a < b)
Surface area: S
S = 2 Pi b(b+a arcsinh[be/a]/[be/a]),
where e = sqrt(b^{2}a^{2})/b

To read more, visit:
The Geometry Center:
Quadrics
Eric Weisstein's World of Mathematics:
Ellipsoid
Prolate Spheroid
Oblate
Spheroid

Circular or Ring Torus
The surface of a threedimensional
figure shaped like a doughnut. 
Major radius (of the large circle): R
Minor radius (of circular crosssection): r
Surface area: S
Volume: V
S = 4 Pi^{2}Rr
V = 2 Pi^{2}Rr^{2} 

To read more, visit:
The Geometry Center:
Torus
Eric Weisstein's World of Mathematics:
Torus

Spherical Polygon
A closed geometric figure on the surface
of a sphere formed by the arcs of great circles. 
Radius: r
S = (theta[n2]Pi)r^{2} = (alpha180[n2])Pi r^{2}/180
Number of sides: n
Sum of Angles: theta (in radians),
alpha (in degrees)
Surface area: S 

spherical triangle

spherical quadrilateral

To read more, visit:
Eric Weisstein's World of Mathematics:
Spherical
polygon
Great circle
Spherical
triangle

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