This paper presents the problem of efficient shaping spherical structures geodesic domes, which is basis for creating a regular octahedron, in aspect sustainable development. The proposed two methods covered by this study differ way dividing points initial edges octahedron are connected, and, therefore, sphere shaped. Using different methods, families domes with lengths struts but similar numbe...

It is proved that a graph does not contain an octahedron minor if and only if it is constructed from {K1,K2,K3,K4}∪{C 2 2n−1 : n ≥ 3} and five other internally 4-connected graphs by 0-, 1-, 2-, and 3-sums.

We prove that all 3-connected 4-regular planar graphs can be generated from the Octahedron Graph, using three operations. We generated these graphs up to 15 vertices inclusive. Moreover, by including a fourth operation we obtain an alternative to a procedure by Lehel to generate all connected 4-regular planar graphs from the

We build unbounded classes of plane and projective plane multiwheels that are 4-critical that are received summing odd wheels as edge sums modulo two. These classes can be considered as ascending from single common graph that can be received as edge sum modulo two of the octahedron graph O and the minimal wheel W3.

In the title complex, [Ni(C(14)H(12)N(3)O)(2)], the Ni(II) atom lies at the centre of a distorted octahedron formed by two tridentate hydrazone ligands. Inter-molecular hydrogen bonds of the type C-H⋯X (X = N, O) link the complexes into a two-dimensional network.

In this article we present a structural characterization of graphs without K5 and the octahedron as a minor. We introduce semiplanar graphs as arbitrary sums of planar graphs, and give their characterization in terms of excluded minors. Some other excluded minor theorems for 3-connected minors are shown.