Re: Sphere inside a pyramid

In article <W8SdnfowyfKGGbHeRVn-ug@xxxxxxxxxxxxxx>,
"odin" <ragnarok@xxxxxxxxx> wrote:

> >> What is the equation of the sphere inside a pyramid of unequal sides such
> >> that each surface of the pyramid is tangent to the sphere?
> >
> > In general there won't be one.
>
> True. It would be like asking what circle fits in an arbitrary rectangle
> such that each side is a tangent to the circle. Only squares work.

Lots of non-square quadrilaterals work for inscribing circles!

For example, every equilateral quadrilateral (rhombus) works.

In three dimensions, a sphere may be inscribed in a pyramid if and only
if there are normals to each face, including the base, which are all
concurrent and that point of concurrency is equidistant from all faces.
.

Relevant Pages

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