Prism (EntityClass, 5)
From Hi.gher. Space
(Difference between revisions)
m |
|||
| Line 7: | Line 7: | ||
The first term in the RHS of this equation corresponds to the elements of the base that get duplicated and form the "ends" of the prism, and the second term corresponds to the elements that get extruded (and hence are also prisms) and form the "sides" of the prism. | The first term in the RHS of this equation corresponds to the elements of the base that get duplicated and form the "ends" of the prism, and the second term corresponds to the elements that get extruded (and hence are also prisms) and form the "sides" of the prism. | ||
| + | |||
| + | Notice that the only difference from the equation for [[pyramid]]s is the coefficient of the first term. | ||
Revision as of 15:40, 11 March 2011
A prism is a shape which has been constructed by extrusion.
There is a simple relationship between the numbers of elements of a prism, and the numbers of elements of its base:
Hn(+A) = 2Hn(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 prism.
The first term in the RHS of this equation corresponds to the elements of the base that get duplicated and form the "ends" of the prism, and the second term corresponds to the elements that get extruded (and hence are also prisms) and form the "sides" of the prism.
Notice that the only difference from the equation for pyramids is the coefficient of the first term.
