(1) Design of sphere_Drawing a regular polyhedron on a sphere

 How can we draw Platonic solids on a sphere?

First, it is easy to mark the first point on the ball pit. However, it is not easy to find the location of the second point on the regular polyhedron. Furthermore, even if two points are marked, it is difficult to draw a straight line (in fact, a curve) on the sphere connecting these two points.


However, if you use [Spherical octacu] and [Spherical icodo], and a [great circle ruler], you can easily draw a spherical regular polyhedron.

[Spherical octacu]


[Spherical icodo]


[great circle ruler]


 After inserting the ballpoint pen into [Spherical octacu], mark all the marked holes with a name pen as shown in the enlarged photo below. These are the vertices of a regular octahedron. Mark all the unmarked holes with a name pen. These are the vertices of a regular cube.


Likewise, if you put a ball in [Spherical icodo] and use a name pen to mark all the dots in the marked holes in the enlarged photo below, they are the vertices of a regular icosahedron, and if you mark all the dots in the unmarked holes, they are the vertices of a regular dodecahedron.


You can easily follow the instructions for using the sphere [great circle ruler] by referring to the picture below.



Now, let's draw five regular polyhedra on the sphere using [Spherical octacu] and [Spherical icodo] and the [great circle ruler].

 

①　Tessellation using the great circle of a cube

You can draw a spherical tetrahedron by selecting 4 of the 8 vertices of a spherical cube and connecting them. If you connect the adjacent red dots in the first picture below, you can draw a spherical tetrahedron as in the second and third pictures. (Because it is a tetrahedron on a sphere, it may not be clearly visible in the picture.)

Spherical tetrahedron



Spherical cube


Spherical octahedron


Spherical dodecahedron

Spherical icosahedron



In the following article, we will create various designs using the vertices of five types of regular polyhedra printed on a sphere.

 

Ⓒ msolid 






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