Thread: Volume & Surface Area of a pyramid within an isohedron

Hi Maths heads

I want to find the mathmatical formula for a pyramid within a sphere.
Consider a spere of any radius R
I want to cut out a pyramid with vertex at the centre of the sphere and the cutting through the sphere at radius R
The angle between the opposite planes of the vertex is 'theta'

ie the volume of the pyramid must be a multiple wjole number 'n'.

Also the surface area of the base of the pyramid which is part of the curved surface area of the sphere is to be the same multiple of the surface area of the sphere.

I am tryoing to work out an easy formula for a isohedron where the sphere is divided into a square pattern and therefore the shere is divided fully into these square units.

As i cannot draw a diagram here, any clarifications would be welcome.

Thanks....

To clarify the base of the pyramid is dome shaped and follows the curvature of the sphere surface.