What are the six-sided figures called?
A six-sided polygon or 6-gon is a hexagon.The total of the internal angles of a hexagon is 720.
A regular hexagon has Schlfli symbol 6 and can be constructed as a truncated equilateral triangle, t3, which alternates two types of edges.
A regular hexagon can be either equilateral or equiangular.It has an inscribed circle and a circumscribed circle.
The common length of the sides is the same as the circle's apothem.The internal angles are 120 degrees.The dihedral group D6 is made up of six symmetries and six lines of symmetry.The longest diagonals of a regular hexagon are twice the length of one side.The regular hexagon can be partitioned into six equilateral triangles if there is a triangle at the center of it.
Like squares and equilateral triangles, regular hexagons fit together without gaps to tile the plane and are useful for constructing tessellations.The hexagonal shape of the honeycomb's cells makes use of space and building materials more efficiently.The honeycomb tessellation of hexagons is depicted in the Voronoi diagram.Although it is equilateral, it isn't usually considered a triambus.
The side length is t and the maximal diameter is D, which corresponds to the long diagonal of the hexagon.
The area can be expressed in terms of the apothem a and the perimeter p.
The regular hexagon fills the fraction 3 3 2 0.8270 and it's circumscribed circle.
If a regular hexagon has any of the following: A, B, C, D, E, F, and if P is a point on the circum circle between B and C.
The height-to-width ratio of a regular hexagon is 1: 1.1547005, which means a long diagonal of 1.0000000 will have a distance between parallel sides.
For an arbitrary point in the plane of a regular hexagon with circumradius R, whose distances to the centroid of the regular hexagonal and its six vertices are L and d.
If the distances from the vertices of a regular hexagon to any point on its circums circle are displayed as displaystyle d_i, then that's right.
The regular hexagonal has Dih6 symmetry.There are three dihedral groups: Dih1, DiH2, and Z6.
There are nine distinct symmetries of a regular hexagon.These are labeled by a letter and group order.r12 is full symmetry and a1 is not.p6, an isogonal hexagon constructed by three mirrors can alternate long and short edges, and d6, a isotoxal hexagonal constructed with equal edge lengths, can have two different internal angles.Half the symmetry order of the regular hexagon can be found in these two forms.Regular hexagons are stretched along one symmetry direction in the i4 forms.The kites can be seen as either rhombus or d2 and p2 kites.hexagonal parallelogons are also called g2 hexagons.
The subgroup symmetry allows for more freedom for irregular forms.The g6 subgroup has no degrees of freedom but can be seen as directed edges.
The symmetry g2, i4, and r12 can be tessellated by parallelogons.The plane can be tiled with different orientations.
The hexagonal pattern of the Lie group A2 is represented by a Dynkin diagram.The two roots have the same angle.
The Dynkin diagram shows the 12 roots of the group G2 in a hexagonal pattern.The roots of two lengths have the same angle.
According to Coxeter, every zonogon can be divided into two parallelograms.The parallelograms are all rhombi for regular polygons with evenly many sides.A cube with 3 of 6 square faces is used as the basis for the decomposition of a regular hexagon.The cube has parallelogons and projective directions.
A regular hexagon has a Schlfli symbol.A regular hexagon is a part of the regular hexagonal tiling.
A truncated equilateral triangle can be created with the Schlfli symbol.This form only has D3 symmetry and is seen with two types of edges.
A truncated hexagon is a dodecagon with two types of edges.An equilateral triangle, 3, is an alternated hexagon.A regular hexagonal can be created with equilateral triangles on its edges.Adding a center point can make a regular hexagon into six equilateral triangles.This pattern is repeated within the triangular tiling.
Adding alternating squares and equilateral triangles around a regular hexagonal dodecagon can extend it.This pattern is repeated within the tiling.
Hives are prevalent in nature due to their efficiency.If a large area is to be filled with the fewest hexagons, each line is as short as it can possibly be.Under compression, honeycombs need less wax to build and gain strength.
Irregular hexagons with parallel opposite edges can be tiled by translation.In three dimensions, hexagonal prisms with parallel opposite faces are called parallelohedrons.
The regular hexagon is what determines a unique tessellation of the plane.
If an intersection with an arbitrary hexagon and pairs of opposite sides are extended until they meet, the three points will lie on a straight line.
The three lines that are parallel to the edges that pass through the symmedian point of the Lemoine hexagon are inscribed in a circle.
The three main diagonals intersect in a single point if the ace is bdf.[5]
The segments connecting the circumcenters of opposite triangles are concurrent if the adjacent sides are extended to their intersection.[6]
The area of the hexagon is twice as big as the triangle at the six points where the extended altitudes meet the circum circle.179
ABCDEF is a hexagonal formed by six lines of a conic section.The three main diagonals are AD, BE, and intersect at a single point.
If an equilateral triangle is built on each side of a hexagon, then the segments connecting the centroids of the opposite triangles form another triangle.1
A skew hexagon has six edges but is not on the same plane.The interior of an hexagon is not generally defined.A skew zig-zag hexagon has two parallel planes.
A regular skew hexagon has the same edge lengths.In three dimensions it will be a zig-zag skew and can be seen in the edges of a triangular antiprism with the same D3d, [2+,6] symmetry.
The cube is similar to the triangular antiprism in that it has regular skew hexagons.
The regular skew hexagon is shown in the skew orthogonal projections.
The principal diagonal of a hexagon divides it into two parts.There is a principal diagonal d1 in any equilateral hexagon with all sides equal.
There is no Platonic solid made of only regular hexagons because they don't allow the result to "fold up".There are some hexagonal faces in the Archimedean solids.Coxeter diagrams of the form and truncated triangles can be found on these hexagons.
There are polyhedra with stretched or flattened hexagons.
There are naturally formed basalt columns from Giant's Causeway in Northern Ireland.
There is a vaguely hexagonal shape in Metropolitan France.The European mainland of France is referred to in French as l'Hexagone.