perplexus.info :: Shapes : Cube vs Octahedron sphere covering

Cube vs Octahedron sphere covering (Posted on 2025-02-28)

A small sphere is centered at a corner of a large cube. What proportion of the surface of the sphere is inside of the cube?

Answer the same question with the cube replaced with a regular octahedron.

No Solution Yet Submitted by Jer

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re(2): Possible answer

| Comment 4 of 6 |

(In reply to re: Possible answer by Jer)

OK, I'm convinced.

But which of my assumptions was wrong.

1) that the sum of all the solid angles is 4π steradians for all polyhedra

2) that all the solid angles in a regular octahedron are symmetric ?

Posted by Larry on 2025-03-01 11:16:32

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