bipyramid

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bipyramid

[¦bī¦pir·ə‚mid]
(crystallography)
A crystal having the form of two pyramids that meet at a plane of symmetry. Also known as dipyramid.
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In particular, this applies to the case that P = [-1, 1] [direct sum] Q is a proper bipyramid over a (d - 1)- dimensional lattice polytope Q.
The direct sum of several intervals with a polytope Q is the same as an iterated proper bipyramid over Q.
Note that, up to lattice isomorphism, there are only two choices for v, either 0, which gives a proper bipyramid, or some vertex, which results in a skew bipyramid.
over the regular bipyramid over Q is a direct product with the projective line [P.
6] or to a skew bipyramid over a (d - 1)-dimensional smooth Fano polytope with 3(d - 1) - 1 = 3d - 4 vertices.
The final case in this section differs from the above in that the base vertex of the second skew bipyramid is an apex of the first stage.
36) we show that in this case P, again, must be a skew bipyramid.
In the first two cases the first stage is a proper bipyramid.
P] [member of] H(F, 1) there is only one choice of a double bipyramid where both stages are skew.