## Cupola

An -gonal cupola (possible for only , 4, 5) is a Polyhedron having Triangular and Square faces separating an and a Regular Polygon. The coordinates of the base Vertices are

 (1)

and the coordinates of the top Vertices are
 (2)

where and are the Circumradii of the base and top
 (3) (4)

and is the height, obtained by letting in the equations (1) and (2) to obtain the coordinates of neighboring bottom and top Vertices,
 (5) (6)

Since all side lengths are ,
 (7)

Solving for then gives
 (8)

 (9)

 (10)

See also Bicupola, Elongated Cupola, Gyroelongated Cupola, Pentagonal Cupola, Square Cupola, Triangular Cupola

References

Johnson, N. W. Convex Polyhedra with Regular Faces.'' Canad. J. Math. 18, 169-200, 1966.