Page 80 - NUMINO Challenge_D1
P. 80
Basic Concepts Soccer Ball
The following figure is a regular icosahedron. 5 faces meet at each vertex,
so 5 edges are connected at each vertex. The 1 point of each edge,
3
starting from each vertex, is cut out. The new solid figure has the shape of a
soccer ball.
Example Find the number of faces, edges, and vertices that the soccer ball
has.
Class Notes
There are 20 faces, 30 edges, and 12 vertices in a regular icosahedron.
The solid figure that is cut out at each vertex of a regular icosahedron is a pentagonal
pyramid with a base that has the shape of a . If 1 pentagonal pyramid is
cut out, the number of faces, edges, and vertices increases by 1, 5, and 4, respectively.
12 pentagonal pyramids are cut out to make a soccer ball. The numbers of faces,
edges, and vertices are shown below.
Faces: 20 1 12
Edges: 30 12 Vertices: 12 12
You can use another method to find the number of vertices and edges for a soccer ball.
A soccer ball has 20 regular hexagons made from cutting the triangles and
regular pentagons made from cutting the vertices of a regular icosahedron.
Therefore, the total number of faces is .
The sums of the numbers of edges and vertices of the pentagons and hexagons are
shown below.
Edges: 6 5 12 180 Vertices: 6 20 5 180
3 faces meet at each vertex of a soccer ball, and 2 faces meet at each edge of a soccer
ball.
Edges: 180 2 Vertices: 180 3
77Geometry
The following figure is a regular icosahedron. 5 faces meet at each vertex,
so 5 edges are connected at each vertex. The 1 point of each edge,
3
starting from each vertex, is cut out. The new solid figure has the shape of a
soccer ball.
Example Find the number of faces, edges, and vertices that the soccer ball
has.
Class Notes
There are 20 faces, 30 edges, and 12 vertices in a regular icosahedron.
The solid figure that is cut out at each vertex of a regular icosahedron is a pentagonal
pyramid with a base that has the shape of a . If 1 pentagonal pyramid is
cut out, the number of faces, edges, and vertices increases by 1, 5, and 4, respectively.
12 pentagonal pyramids are cut out to make a soccer ball. The numbers of faces,
edges, and vertices are shown below.
Faces: 20 1 12
Edges: 30 12 Vertices: 12 12
You can use another method to find the number of vertices and edges for a soccer ball.
A soccer ball has 20 regular hexagons made from cutting the triangles and
regular pentagons made from cutting the vertices of a regular icosahedron.
Therefore, the total number of faces is .
The sums of the numbers of edges and vertices of the pentagons and hexagons are
shown below.
Edges: 6 5 12 180 Vertices: 6 20 5 180
3 faces meet at each vertex of a soccer ball, and 2 faces meet at each edge of a soccer
ball.
Edges: 180 2 Vertices: 180 3
77Geometry
