24.03.2020 | Constructing Platonic Solids

The platonic solids represented in this class were:

Tetrahedron (4 triangle faces)

Hexahedron (6 square faces)

Octahedron (8 triangle faces)

Dodecahedron (12 pentagon faces)

Icosahedron (20 triangle faces)

Using 3DRotate, 3D Mirror, Array, and Align commands.

Array command creates copies of objects arranged in a pattern.

Align command aligns objects with other objects in 2D and 3D.

For the tetrahedron, the first step was to create a 2D net of the solid. The tetrahedron net consists of four equilateral triangles.

A vertical line is drawn at the center of the middle triangle.

A circumference is then made touching the bottom triangle’s vertex and the vertex of the opposite triangle to this one.

Using the command 3DRotate the circumference is rotated so it is perpendicular to the face we wish to fold. After this, the first face is folded using the Align command.

This process is then repeated for each of the remaining faces using the array command until the tetrahedron gains its form.

For the hexahedron, also known as a cube, the net consists of six squares. 
To form the solid, simply use the command 3D rotate and bend the faces at an angle of 90º.

The octahedron can is done by starting with a square in the center surrounded with four triangles on each side.

The process of the tetrahedron is repeated here until the four faces are aligned.

After having this solid completed we use the 3DMirror command and place the mirrored object in its base, which forms the octahedron solid. 

Twelve regular pentagons compose the dodecahedron, a more complex solid than the previous ones. 

Starting with three of the pentagons attached to the middle one lines are drawn in the intersections and joined with perpendicular lines. To find the intersection point of the pentagon faces two circumferences are used.

Having this, the process of folding the faces using Align and Array is used as in the previous solids.

The result is a half shell of the dodecahedron. Using align, a copy of this shell is placed on top, fitting perfectly in the opposite vertices of the bottom one.

The icosahedron net is composed of a central pentagon with five triangles in each face. 

Having the net the process of folding is once again the same as the other solids. When this is done the first part of the first half of the solid is done.

Having this, a triangle is drawn on one of the previous placements and folded downwards using the same process. The first part is copied and placed on either side of the triangle. This process is repeated until the icosahedron is completed.