Pyramid (EntityClass, 5)
From Hi.gher. Space
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<[#ontology [kind class] [cats Construction Shape]]> | <[#ontology [kind class] [cats Construction Shape]]> | ||
| - | A '''pyramid''' is a shape which has been constructed by [[tapering]]. | + | A '''pyramid''' is a shape which has been constructed by [[tapering]]. All pyramids are self-dual. |
There is a simple relationship between the numbers of [[element]]s of a pyramid, and the numbers of elements of its base: | There is a simple relationship between the numbers of [[element]]s of a pyramid, and the numbers of elements of its base: | ||
Revision as of 15:56, 11 March 2011
A pyramid is a shape which has been constructed by tapering. All pyramids are self-dual.
There is a simple relationship between the numbers of elements of a pyramid, and the numbers of elements of its base:
Hn(+A) = Hn(A) + Hn-1(A)
where Hn(X) is the number of n-dimensional elements of the shape X, A is the base shape and &A is the pyramid.
The first term in the RHS of this equation corresponds to the elements of the base that form the "base" of the pyramid, and the second term corresponds to the elements that get tapered (and hence are also pyramids) and form the "sides" of the pyramid.
Notice that the only difference from the equation for prisms is the coefficient of the first term.
