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Stars and Crosses
Oct. 28th, 2019 07:50 pmhttps://emmanuelg.dreamwidth.org/file/6495.jpg
Some geometric solids make a person ponder, and this one certainly does that for me--
I started by cutting all the corners off a cube. This left me with a 14-sided solid made of six squares and eight triangles. If you extend the 14 faces beyond the solid, using only squares and triangles, you get this curious solid, made of the intersections of six crosses and eight six-pointed stars--Still 14 faces. Each cross has a pyramid in the middle of it (or half of an octahedron if you prefer). Each six-pointed star has half of the truncated cube in its centre--Three squares and 4 triangles, or seven faces.
The eight points of the cube are also truncated and colored purple--I don't know why, just seemed like the right thing to do!
Although I meant to generate this solid from the intersection of a cube and octahedron, you could also get it by intersecting two tetrahedrons at right angles to each other with an octahedron, provided you cut off the edges and tips of the tetrahedrons...
Anyway, I like this shape a lot! Although I came up with it independently while playing with geometric solids, it would be difficult to believe that no one else has made one of these first. Perhaps it has a formal geometric name. I'd like to know the formal name, if anyone knows it....
Some geometric solids make a person ponder, and this one certainly does that for me--
I started by cutting all the corners off a cube. This left me with a 14-sided solid made of six squares and eight triangles. If you extend the 14 faces beyond the solid, using only squares and triangles, you get this curious solid, made of the intersections of six crosses and eight six-pointed stars--Still 14 faces. Each cross has a pyramid in the middle of it (or half of an octahedron if you prefer). Each six-pointed star has half of the truncated cube in its centre--Three squares and 4 triangles, or seven faces.
The eight points of the cube are also truncated and colored purple--I don't know why, just seemed like the right thing to do!
Although I meant to generate this solid from the intersection of a cube and octahedron, you could also get it by intersecting two tetrahedrons at right angles to each other with an octahedron, provided you cut off the edges and tips of the tetrahedrons...
Anyway, I like this shape a lot! Although I came up with it independently while playing with geometric solids, it would be difficult to believe that no one else has made one of these first. Perhaps it has a formal geometric name. I'd like to know the formal name, if anyone knows it....
