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stellated octahedron

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The tetrahedron is self-dual, so the dual compound of a tetrahedron with its dual is the regular stellated octahedron.
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Thus it is a stellation of the octahedron, and in fact, the only finite stellation thereof.
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Here we can see an adaptation of the stellated octahedron (stella octangula).
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stellated octahedron was drawn by Leonardo for Luca Pacioli's book 'De Divina Proportione'.
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The stellated octahedron can be seen either as a polyhedron compound or as a stellation.
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Five Platonic Solids stellated octahedron was drawn by Leonardo for Luca Pacioli's book 'De Divina Proportione'.
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Then the volume of an stellated octahedron of side length a is:
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The stellated octahedron was drawn by Leonardo for Luca Pacioli's book 'De Divina Proportione'.
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Leonardo da Vinci: Drawing of an stellated octahedron (stella octangula) made to Luca an adaptation of the stellated octahedron (stella octangula).
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Leonardo da Vinci: Drawing of an stellated octahedron (stella octangula) Here we can see an adaptation of the stellated octahedron (stella octangula).
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Leonardo da Vinci: Drawing of an stellated octahedron (stella octangula) made we can see an adaptation of the stellated octahedron (stella octangula).
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Figure 1: Stellated octahedron and its inner grid (click on the left image to get a 3D view that you can zoom and rotate).
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Then is very easy to calculate the volume of an stellated octahedron if we know the volume of an octahedron and the volume of a tetrahedron.
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The stellated octahedron is at the core of the inner grid of Metatron's Cube, which can be constructed by making a square of four such polyhedra, and another square on top of it.
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(b) To obtain the full grid, one has to also stellate the small octahedrons in the middle of the big tetrahedrons that themselves stellate the big central octahedron.
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The complete grid inside Metatron's Cube results from stellating all those octahedrons.
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As an stellation is an octahedron with tetrahedral pyramids on each face.
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It contains an octahedron in the middle, and eight tetrahedrons which stellate every face of this central octahedron.
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That made me think that the star tetrahedron, which is the stellation of the octahedron, could also be a building block of Metatron's Cube.
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One solution, which is not optimum in terms of volume but preserves the previous reorderings, would be to start from the ten ball tetractis of Figure 4 and go on stellating the octahedron until reaching a star tetrahedron (Figure 6).
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In order to obtain the full grid inside Metatron's Cube starting from this big octahedron, one must follow two steps: in the first step, you stellate the big octahedron, obtaining a big star tetrahedron that is also contained in the cube's grid (Fig.14a).
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As a stellation, it is constructed starting from an octahedron by adding small tetrahedra on each face.
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The compound polyhedron of a cube and an octahedron is an stellated cuboctahedron.It is the same to say that the cuboctahedron is the solid common to the cube and the octahedron in this polyhedron.
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(a) The big central octahedron can also be stellated (only one face shown) giving rise to a big star tetrahedron that is also present in the grid inside Metatron's cube.
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The first stellation of the cuboctahedron is the compound of a cube and its dual octahedron, with the vertices of the cuboctahedron located at the midpoints of the edges.
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27 sinne gevind in 10 ms. Hulle kom uit baie bronne en word nie nagegaan nie.