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All internal angles are 120 degrees. A regular hexagon has six rotational symmetries (rotational symmetry of order six) and six reflection symmetries (six lines of symmetry), making up the dihedral group D 6. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side.
If six unordered points are given on a conic section, they can be connected into a hexagon in 60 different ways, resulting in 60 different instances of Pascal's theorem and 60 different Pascal lines. This configuration of 60 lines is called the Hexagrammum Mysticum. [3] [4]
The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...
The opposite angle, between long edges, is arccos(-5+9 √ 5 / 40 )≈67.783011547435° . The other two angles of each face, between a short and a long edge each, are both equal to arccos( 5-2 √ 5 / 10 )≈86.97415549104°. The dihedral angle between any pair of adjacent faces is arccos(-19-8 √ 5 / 41 )≈154.12136312578°.
The term "isometric" comes from the Greek for "equal measure", reflecting that the scale along each axis of the projection is the same (unlike some other forms of graphical projection). An isometric view of an object can be obtained by choosing the viewing direction such that the angles between the projections of the x , y , and z axes are all ...
An equilic quadrilateral has two opposite equal sides that when extended, meet at 60°. A Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length. [6] A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7]
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An angle equal to 0° or not turned is called a zero angle. [5] An angle smaller than a right angle (less than 90°) is called an acute angle [6] ("acute" meaning "sharp"). An angle equal to 1 / 4 turn (90° or π / 2 radians) is called a right angle. Two lines that form a right angle are said to be normal, orthogonal, or ...