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What is Hexagon?

Hexagon

Hexagon comes from Greek terminology. ‘Hex’ means ‘six’ and ‘gon’ means ‘corner or angle’, thus for the six sides this figure is known as ‘Hexagon’. This also can be described as the six-sided or 6-gon. A regular hexagon can also be made out of the internal angles of a truncated equilateral triangle which has alternated two types of edges. 

Thus, a regular hexagon can be defined as a hexagon that is both equilateral and equiangular in nature. Hexagon is bicentric as well, this means, it has both circumscribed circle and also an inscribed circle.   

Hexagon has a common length of sides which is equal to the radius of the circumscribed circle or the circumcircle. While all the internal angles of a hexagon are 120 degrees. 

The longest diagonals of a regular hexagon will connect to the opposite vertices in a diametrical structure, this will measure two times the length of one side. 

From this viewpoint, it can be seen that a triangle with a vertex at the central point of the regular hexagon has a sharing at one side with the hexagon which is equilateral and this is the regular hexagon that can be partitioned into six other equilateral triangles.

What is a Regular Hexagon?

A regular hexagon fits together without any gaps (which will tile the plane; these are the three hexagons that will meet at every vertex) thus this is for use for constructing the tessellations. The cells that are formed of a beehive honeycomb are hexagonally designed for making efficient use of space and building the materials. This is the Voronoi diagram which is of a regular triangular lattice which is a honeycomb tessellation of the hexagons. This is usually not considered as a triambus, even though this is an equilateral. 

What is Dodecahedron?

In geometry, dodecahedrons have twelve flat faces polyhedron. This is the most popular dodecahedron with regular pentagons as its face sides, this is a Platonic Solid. There are also three sets of regular star dodecahedra which are being constructed as the stellations of the convex form structure. All of these have an icosahedral symmetry with the order of 120.  

Some dodecahedra also have the same combinatorial structure which has the regular dodecahedron but they have their pentagonal faces which are not regular to each other. 

Properties of Dodecahedron

Now we will learn some of the important properties, which will constitute the sides, edges, shapes, vertices, and angles that are related to the dodecahedron.

  1. Sides – A dodecahedron structure has a total of 12 pentagonal sides.
  2. Edges – A dodecahedron consists of 30 edges.
  3. Vertices – It has 20 Vertices, which means corner points, and they have each vertex of 3 edges that meet together.
  4. The structure has 160 diagonals.  
  5. The formula to calculate the sum at each vertex of the structure is – 3 x 108° = 324°.
  6. Angles – The angles which are located between the sides of the pentagon is 108° and the angle of intersection has 2 adjacent faces with an angle of: 116.56505°.
  7. Shapes – the shape of the dodecahedron can be seen in many actual life situations like in the Roman dodecahedron, dodecahedron dice, and many more.

Some Facts on Dodecahedron

  1. Tetrahedron, cube, octahedron, icosahedron, and dodecahedron are the only 5 types of solid platonic figures. 
  2. While an icosahedron has 20 maximum number of faces.
  3. The dodecahedron and icosahedron have an equal number of edges, i.e., 30.
  4. The icosahedron is known as the dual of the dodecahedron which has the same number of edges. Also, the icosahedron is the platonic-shaped structure that has the largest number of faces and it also has the largest volume of all the platonic solid structures.
  5. According to the Greek Philosopher named Plato, the tetrahedron symbolized the fire element. The dodecahedron symbolizes the universe.  

We will not stop here, if interested in further exploration, visit Cuemath for more insights regarding the same topic.

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