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# How to make the right dodecahedron

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A dodecahedron is a regular polyhedron,Whose faces are twelve regular pentagons. The simplest for constructing a regular polyhedron is a hexahedron or a cube, all the other polyhedra can be constructed by inscribing or describing them around it.

A dodecahedron can be constructed by describing it near a cube.

Instructions

1

Construct a cube with edge length a. Calculate the length of the dodecahedron under construction using the formula: m = -a / 2 + av5 / 2, where a is the length of the edge of the cube.

2

On the SPRQ face, draw a line K1L1 connecting the middle of the edges. On this line, postpone a segment of length m equidistant from the edges of the cube. Through the ends of the segment, draw perpendiculars to the face of SPRQ.

3

Construct the pentagon ABCDE with the diagonals AC and BE. AB = BC = a. Calculate the height of the triangle ABC and designate it s = BN.

4

On perpendiculars, find the points, the distance from which to the midpoints of the edges is s, that is, LL1 = KK1 = s. Now connect the found points to the vertices of the cube.

5

Repeat constructions 2 and 4 for each face, as a result you will get the right polyhedron described near the cube - the dodecahedron.

How to make the right dodecahedron Was last modified: May 21st, 2017 By
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