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Octahedron creation

Posted Oct 5, 2015, 10:41 a.m. EDT Geometry Version 4.4 2 Replies

Davide Marano
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I need to create by the Comsol geometry builder, an octaedron having a face lying on a plane.
I created the octaedron merging two pyramids, but i'm not able to rotate it in such a way that a face lies on a desired plane.
Is there anyone who can help me?
Thanks in advance
2 Replies Last Post Oct 7, 2015, 10:03 a.m. EDT
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 9 years ago Oct 5, 2015, 2:32 p.m. EDT
Hi

If I read Wiki right a octahedron inscribed in a circle of radius "R" has side edges of length "sqrt(2)*R" and can be made up of 8 tetrahedrals, all with a common vertex at the 0,0,0 coordinate.

So if you start to draw a triangle equilateral based on a circle of radius sqrt(2)*R, on two plane R/sqrt(2) below and above the origin, and then draw a sphere of radius R centered at 0,0,0 you should be able to finish, no ?

The dual of the octahedron being a cube (point centered at each face of a cube) of side 2*R this should also help to get it right.

The dihedral angle is acos(-1/3), check it out

--
Good luck
Ivar
Hi If I read Wiki right a octahedron inscribed in a circle of radius "R" has side edges of length "sqrt(2)*R" and can be made up of 8 tetrahedrals, all with a common vertex at the 0,0,0 coordinate. So if you start to draw a triangle equilateral based on a circle of radius sqrt(2)*R, on two plane R/sqrt(2) below and above the origin, and then draw a sphere of radius R centered at 0,0,0 you should be able to finish, no ? The dual of the octahedron being a cube (point centered at each face of a cube) of side 2*R this should also help to get it right. The dihedral angle is acos(-1/3), check it out -- Good luck Ivar
Davide Marano
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Posted: 9 years ago Oct 7, 2015, 10:03 a.m. EDT
Thank you so much. I did it.
Davide
Thank you so much. I did it. Davide

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