Fig.1 is a solid of which surface consists of four equilateral triangles of the same size and this solid is called a regular tetrahedron.
Fig. 2 is a solid of which surface consists of six squares of the same size and this solid is called a cube.
Fig. 3 is a solid of which surface consists of eight equilateral triangles of the same size and this solid is called a regular octahedron.
Fig. 4 is a solid of which surface consists of 12 equilateral pentagons of the same size and this solid is called a regular dodecahedron.
Fig. 5 is a solid of which surface consists of 20 equilateral triangles of the same size and this solid is called a regular icosahedron.
Fig. 2 is a solid of which surface consists of six squares of the same size and this solid is called a cube.
Fig. 3 is a solid of which surface consists of eight equilateral triangles of the same size and this solid is called a regular octahedron.
Fig. 4 is a solid of which surface consists of 12 equilateral pentagons of the same size and this solid is called a regular dodecahedron.
Fig. 5 is a solid of which surface consists of 20 equilateral triangles of the same size and this solid is called a regular icosahedron.
It is considered that sides of these solid is cut by a cutter to be a development view.
Only the side is cut and a development view should not be separated into two or more sheets.
It is considered how many sides should be cut.
(Example)
In Fig. 1, if three sides are cut, it will become as it is shown in Fig. 6 or Fig. 7.
Since it will be separated into two sheets if four sides are cut as shown in Fig. 8, it does not suit conditions.
Therefore, the number of the sides to be cut is 3.
Find number of the sides which should be cut, respectively in the case of Fig. 2, Fig. 3, Fig. 4, and Fig. 5.
Only the side is cut and a development view should not be separated into two or more sheets.
It is considered how many sides should be cut.
(Example)
In Fig. 1, if three sides are cut, it will become as it is shown in Fig. 6 or Fig. 7.
Since it will be separated into two sheets if four sides are cut as shown in Fig. 8, it does not suit conditions.
Therefore, the number of the sides to be cut is 3.
Find number of the sides which should be cut, respectively in the case of Fig. 2, Fig. 3, Fig. 4, and Fig. 5.
Answer
Fig.2 7
Fig.3 5
Fig.4 19
Fig.5 11
Fig.3 5
Fig.4 19
Fig.5 11
Reference
