Search results
Results from the WOW.Com Content Network
A circular triangle is a triangle with circular arc edges. The edges of a circular triangle may be either convex (bending outward) or concave (bending inward). [c] The intersection of three disks forms a circular triangle whose sides are all convex. An example of a circular triangle with three convex edges is a Reuleaux triangle, which can be made
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. [1] In a polygon, an edge is a line segment on the boundary, [2] and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides ...
Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror.
Each pair of triangles gives a path of length three that includes the edge connecting the triangles together with two of the four remaining triangle edges. [3] By applying Petersen's theorem to the dual graph of a triangle mesh and connecting pairs of triangles that are not matched, one can decompose the mesh into cyclic strips of triangles.
To convert a graph with a unique triangle per edge into a triple system, let the triples be the triangles of the graph. No six points can include three triangles without either two of the three triangles sharing an edge or all three triangles forming a fourth triangle that shares an edge with each of them.
Triangle postulate: The sum of the angles of a triangle is two right angles. Playfair's axiom: Given a straight line and a point not on the line, exactly one straight line may be drawn through the point parallel to the given line. Proclus' axiom: If a line intersects one of two parallel lines, it must intersect the other also. [3]
This nine-edge Shannon multigraph requires nine colors in any edge coloring; its vertex degree is six and its multiplicity is three. According to a theorem of Shannon (1949) , every multigraph with maximum degree Δ {\displaystyle \Delta } has an edge coloring that uses at most 3 2 Δ {\displaystyle {\frac {3}{2}}\Delta } colors.
It is very similar to the net for the 5-cell, as the net for a tetrahedron is a triangle with other triangles added to each edge, the net for the 5-cell a tetrahedron with pyramids attached to each face. This interpretation is expressed in the name. The length of the shorter edges is 3 / 5 that of the longer edges. [2]