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Are there Egyptian pyramids which were modeled to resemble half an octahedron? Do the angles of some pyramids correspond to angles of an octahedron?

For those who don't know what an octahedron is: http://en.wikipedia.org/wiki/Octahedron

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    This doesn't make any sense. Half an octahedron is a whole square pyramid.
    – Semaphore ♦
    Oct 27, 2014 at 20:18
  • @Semaphore : Correct. But a square pyramid is not necessarily half an octahedron.
    – user50746
    Oct 27, 2014 at 22:12
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    For example, the polyhedron in this picture is a square pyramid, but it's clearly not half an octahedron: pad1.whstatic.com/images/thumb/f/fc/…
    – user50746
    Oct 27, 2014 at 22:15
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    In short, no. Relevant pages on how the angles were laid out are on Wikipedia and here in more detail.
    – Comintern
    Oct 27, 2014 at 23:28
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    You might read your own Wikipedia reference. An octahedron is a polygon with 8 faces. What you're apparently looking for is a REGULAR octahedron, where all the faces are equilateral triangles. By definition, any pyramid is half of an octahedron.
    – jamesqf
    Jul 15, 2015 at 18:54

2 Answers 2

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For a pyramid to be "half an octahedron", its height must be the width divided by sqrt(2). Examination of the List of Egyptian pyramids shows that this is not the case.

E.g.,

  • Sneferu: 220/(105*sqrt(2)) = 1.481557
  • Khufu: 230.3/(146.6*sqrt(2)) = 1.110823
  • Menkaure: 103.4/(65.5*sqrt(2)) = 1.116257

i.e., they are flatter than "half an octahedron".

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    There is a pyramid that was built too steeply and collapsed. A nearby pyramid had its angle hastily changed and is the "Bent" pyramid.
    – Oldcat
    Oct 27, 2014 at 23:39
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    Even the Bent Pyramid was built half a millennium before the first Egyptian writings on Geometry. Considering that fact that the first two writings happened to be on calculating the area of pyramids, I think the evidence is as conclusive as a person could reasonably hope for that that is the shape they had in mind while building the pyramids.
    – T.E.D. ♦
    Jul 15, 2015 at 17:48
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I suppose the gist of this questions is whether the faces of the pyramids are equilateral triangles. The answer to this question is "no", the faces of the pyramids are not equilateral triangles.

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