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In geometry, a triangular prism or trigonal prism [1] is a prism with 2 triangular bases. If the edges pair with each triangle's vertex and if they are perpendicular to the base, it is a right triangular prism. A right triangular prism may be both semiregular and uniform. The triangular prism can be used in constructing another polyhedron.
In the mathematical field of graph theory, the triangle graph is a planar undirected graph with 3 vertices and 3 edges, in the form of a triangle. [ 1 ] The triangle graph is also known as the cycle graph C 3 {\displaystyle C_{3}} and the complete graph K 3 {\displaystyle K_{3}} .
A graceful labeling. Vertex labels are in black, edge labels in red.. In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some subset of the integers from 0 to m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between 1 and m ...
It can be generated by two elements, a rotation by an angle of 2 π /n and a single reflection, and its Cayley graph with this generating set is the prism graph. Abstractly, the group has the presentation r , f ∣ r n , f 2 , ( r f ) 2 {\displaystyle \langle r,f\mid r^{n},f^{2},(rf)^{2}\rangle } (where r is a rotation and f is a reflection or ...
The graph of the triaugmented triangular prism has 9 vertices and 21 edges. It was used by Fritsch & Fritsch (1998) as a small counterexample to Alfred Kempe 's false proof of the four color theorem using Kempe chains , and its dual map was used as their book's cover illustration. [ 12 ]
1. A book, book graph, or triangular book is a complete tripartite graph K 1,1,n; a collection of n triangles joined at a shared edge. 2. Another type of graph, also called a book, or a quadrilateral book, is a collection of 4-cycles joined at a shared edge; the Cartesian product of a star with an edge. 3.
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Although simple, this formula is only useful if the height can be readily found, which is not always the case. For example, the land surveyor of a triangular field might find it relatively easy to measure the length of each side, but relatively difficult to construct a 'height'. Various methods may be used in practice, depending on what is ...