Position the prism with O at the origin and with a prismatic base in the XY plane.

R is the centre of revolution and is placed on the X-axis.

A, O and B are vertices of the prismatic base.

X, S and S' are equatorial vertices.

Co-ordinates of B are (c, s, 0)

As angle BOS is a right angle then co-ordinates of S are (-as, ac, z) where a<1

As X and S are both equatorial, then co-ordinates of X are (-a, 0 , z)

As distance OX = 1 then

As distance SX = 1 then

This simplifies to give

As the height (H) of the spheno prism is 2z then 

Or as the sin of half of the vertex angle of a polygon is equal to the cosine of half of the central angle, and with the prismatic base as an n-gon, then: