Projection of A Tetrahedron on Platonic Solids

 

around axis 4V around axis 4L
1-1,<R_1> and 3-1,<R_3> 4-1,<R_4 O>

 

Project on a tetrahedron

　

3-fold axis 4V

2-fold axis 4L

1-1,3-1 around 4V

 1-1,3-1

 1-4

4-1 around 4L

1-4

4-1

 

Project on a cube

　

3-fold axis 6V

2-fold axis 6L

4-fold axis 6S

1-1,3-1 around 4V

 1-1,3-1

 1-4

 1-4

4-1 around 4L

 1-4

 2-2

 4-1

 

Project on an octahedron

　

4-fold axis 8V

2-fold axis 8L

3-fold axis 8S

1-1,3-1 around 4V

 1-4

 1-4

 1-1,1-3

4-1 around 4L

 4-1

 2-2

 1-4

 

Project on a dodecahedron

　

3-fold axis 12V

2-fold axis 12L

5-fold axis 12S

1-1,3-1 around 4V

 1-1,3-1

 1-4

 1-4

4-1 around 4L

 1-4

 2-2

 1-4

 

Project on an icosahedron

　

5-fold axis 20V

2-fold axis 20L

3-fold axis 20S

1-1,3-1 around 4V

 1-4

 1-4

 1-1,3-1

4-1 around 4L

 1-4

 2-2

 1-4

 

　 　 4V 4L　 6V 6L 6S 8V 8L 8S 12V 12L 12S 20V 20L 20S
4V 1-1 1-1 1-1 1-1 1-1 1-1 1-1 1-1 1-1 1-1 1-1 1-1 1-1 1-1 1-1
  1-3 1-3 3-1 1-3 1-3 1-3 1-3 1-3 3-1 3-1 1-3 1-3 1-3 1-3 3-1
4L 4-1　 1-4 4-1 1-4 2-2 4-1 4-1 2-2 1-4 1-4 2-2 1-4 1-4 2-2 1-4