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A crossed square is a faceting of the square, a self-intersecting polygon created by removing two opposite edges of a square and reconnecting by its two diagonals. It has half the symmetry of the square, Dih 2 , order 4.
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 ...
Informally: "a box or oblong" (including a square). Square (regular quadrilateral): all four sides are of equal length (equilateral), and all four angles are right angles. An equivalent condition is that opposite sides are parallel (a square is a parallelogram), and that the diagonals perpendicularly bisect each other and are of equal length.
A square pyramid has five vertices, eight edges, and five faces. One face, called the base of the pyramid, is a square; the four other faces are triangles. [2] Four of the edges make up the square by connecting its four vertices. The other four edges are known as the lateral edges of the pyramid; they meet at the fifth vertex, called the apex. [3]
A maximal square in a polygon P is a square in P which is not contained in any other square in P. Similarly, a maximal rectangle is a rectangle not contained in any other rectangle in P. A square s is maximal in P if each pair of adjacent edges of s intersects the boundary of P. The proof of both sides is by contradiction:
In the mathematical field of graph theory, a rhombicosidodecahedral graph is the graph of vertices and edges of the rhombicosidodecahedron, one of the Archimedean solids. It has 60 vertices and 120 edges, and is a quartic graph Archimedean graph. [5] Square centered Schlegel diagram
This example shows 4 blue edges of the rectangle, and two green diagonals, all being diagonal of the cuboid rectangular faces. In spherical geometry, a spherical rectangle is a figure whose four edges are great circle arcs which meet at equal angles greater than 90°. Opposite arcs are equal in length.
Topological square tilings can be made with concave faces and more than one edge shared between two faces. This variation has 3 edges shared. Other quadrilateral tilings can be made which are topologically equivalent to the square tiling (4 quads around every vertex). A 2-isohedral variation with rhombic faces