4Nhedra


Family of convex polyhedra with 4N congruent isosceles triangular faces, for all N>=3.
The solid is formed by an antiprism and two pyramids, and is inscribed into an unitary sphere.
For N=3 the polyhedron degenerates into a cube.
For N=5 the polyhedron is the platonic icosahedron.
For N-->oo the volume --> Pi.


Examples for N=3, 4, 5


Examples for N=7, 12, oo



Table of values


N a b h V
3 .333333 1.632993 .816497 1.539601
4 .414214 1.287189 .870264 2.209139
5 .447214 1.051462 .910593 2.536151
6 .464102 .885782 .935759 2.717968
7 .473952 .764113 .951908 2.82897
8 .480217 .671341 .962752 2.901558
9 .484454 .59841 .970344 2.951567
10 .487457 .539634 .975851 2.98746
11 .489664 .491292 .979964 3.01408
12 .491334 .450848 .983116 3.034364
13 .492628 .416524 .985581 3.050172
14 .493652 .387035 .987546 3.062728
15 .494477 .36143 .989135 3.072867
16 .49515 .338992 .99044 3.08117
17 .495707 .319169 .991524 3.088056
18 .496173 .301531 .992433 3.093829
19 .496567 .285736 .993204 3.098716
20 .496903 .27151 .993863 3.102891
... ............
->oo ->.5 ->0 ->1 ->Pi


5/30/2005 - Livio Zucca

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