Pravilne konkavne kupole druge vrste

Abstract

The term cupola stands for a polyhedron consisting of two regular polygons: n-gon and 2n-gon in parallel planes, connected by an alternating series of squares and equilateral triangles, ie. Johnsonsolids J3, J4 and J5. However, it is possible to form such a cupola that would have a polygon with n ≥ 6 as the starting n-gon, and whose lateral surface is formed by rows of equilateral triangles, constituting a nonconvex polyhedron. The method of forming such a cupola is based on the folding of a net of m x n triangles that form a strip, by whose folding the deltahedral surface is obtained. The cupolae formed by folding the net consisting of two rows of equilateral triangles (with total of 7xn triangles in the lateral surface) are described, and are therefore called cupolae of the second sort, which can have starting polygons from n = 4, to n = 10. The basic parameters of these solids and their geometric interpretation are also given in the paper.

Pod pojmom kupole podrazumeva se poliedar koji se sastoji od dva pravilna poligona: n-tougaonika i 2n-tougaonika u paralelnim ravnima, povezanih naizmenicnim nizom kvadrata i jednakostranicnih trouglova, odn. Dzonsonova tela J3, J4 i J5. Medjutim, moguce je formirati i takvu kupolu koja bi za polazni ntougaonik imala i poligon kod kojeg je n ≥ 6, a ciji bi omotac cinili nizovi jednakostranicnih trouglova, formirajuci pri tome nekonveksni poledar. Nacin formiranja ovakve kupole zasniva se na nabiranju mreze od mxn trouglova koja obrazuje traku, cijim se presavijanjem dobija deltaedarski omotac. Opisane su kupole koje nastaju nabiranjem omotaca koji se sastoji od dva niza (7xn) jednakostranicnih trouglova, te su zato nazvane kupolama druge vrste i koje mogu imati polazne poligone od n=4, do n=10. Dati su i osnovni parametri ovih tela i njihovo geometrijsko tumacenje.