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In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin -derived numerical prefix, rather than hepta-, a Greek -derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning angle.
This is the smallest star polygon that can be drawn in two forms, as irreducible fractions. The two heptagrams are sometimes called the heptagram (for {7/2}) and the great heptagram (for {7/3}). The previous one, the regular hexagram {6/2}, is a compound of two triangles. The smallest star polygon is the {5/2} pentagram.
The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.
Isometric graph paper can be placed under a normal piece of drawing paper to help achieve the effect without calculation. In a similar way, an isometric view can be obtained in a 3D scene. Starting with the camera aligned parallel to the floor and aligned to the coordinate axes, it is first rotated horizontally (around the vertical axis) by ± ...
The dihedral angle of a truncated icosahedron between adjacent hexagonal faces is approximately 138.18°, and that between pentagon-to-hexagon is approximately 142.6°. [ 4 ] The truncated icosahedron is an Archimedean solid , meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in ...
The Fritsch graph is one of only six graphs in which every neighborhood is a 4- or 5-vertex cycle. The dual polyhedron of the triaugmented triangular prism is an associahedron, a polyhedron with four quadrilateral faces and six pentagons whose vertices represent the 14 triangulations of a regular hexagon. In the same way, the nine vertices of ...
Honeycomb (geometry) In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. Its dimension can be clarified as n -honeycomb for a honeycomb of n -dimensional space.
Constructible polygon. In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinitely many constructible polygons, but only 31 with an odd number of sides are ...