__Spheno-prism
height calculation__

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: