# There are an infinite number of regular polyhedra??

• Jul 27th 2009, 02:47 AM
khylenb
There are an infinite number of regular polyhedra??
hi,

Iam new to this forum so hope u peolpe can help. I am in my first year of a 4 yr university course training to be a primary/elementary school teacher.

I have beeen given the statement.. 'there are an infinite number of regular polyhedra'

The statment is said by an 8 yr old child. My task is to identify what is wrong with the statement, and how i would explain to the child the correct statement/ what i could show to the child to make them realise this statement is wrong, ansd the correct course of action to put them on th e right track.

I have been told by my maths teacher the statement is incorrect, but that is all the information i have been given, i dont even know what a rugular polyhedra is!!!

Hope sumone on this forum can help???

Thanks
• Jul 27th 2009, 03:51 AM
HallsofIvy
Quote:

Originally Posted by khylenb
hi,

Iam new to this forum so hope u peolpe can help. I am in my first year of a 4 yr university course training to be a primary/elementary school teacher.

I have beeen given the statement.. 'there are an infinite number of regular polyhedra'

The statment is said by an 8 yr old child. My task is to identify what is wrong with the statement, and how i would explain to the child the correct statement/ what i could show to the child to make them realise this statement is wrong, ansd the correct course of action to put them on th e right track.

I have been told by my maths teacher the statement is incorrect, but that is all the information i have been given, i dont even know what a rugular polyhedra is!!!

Hope sumone on this forum can help???

Thanks

Well, what exactly does that mean? Certainly, you can have a cube with side length n inches for any integer n so there are an infinite number of cubes alone!

A "regular polyheron", also called a "Platonic solid", is a solid figure with all faces the same polygon, all edges the same length, all angles the same.

If you mean "an infinite number of different platonic solids", that is, different numbers of sides, etc., then, far from being an infinite number of them, there are only five of them:

Tetrahedron: Four faces each being an equilateral triangle. Four faces, six edges, four vertices.
Hexahedron (cube): Six faces each being a square. Six faces, twelve edges, eight vertices.
Octahedron: Eight faces, each being an equilateral triangle. Eight faces, twelve edges, four vertices.
Dodecahedron: Twelve faces, each being a regular pentagon. Twelve faces, thirty edges, twenty vertices.
Icosahedron: twenty faces, each being an equilateral triangle. Twenty faces, thirty edges, twenty vertices.

Notice that all of these satisfies "Euler's formula": faces- edges+ vertices= 2.

Also they come in pairs or "duals", swapping number of faces with number of vertices: If you were to mark the center point of each face and then connect those points, the result would be the "dual" polyhedron. The hexahedron is dual to the octahedron, the dodecahedron is dual to the icosahedron and the tetrahedron is dual to itself.

You can see pictures of them here:
Platonic Solid -- from Wolfram MathWorld
• Jul 27th 2009, 04:01 AM
pomp
Quote:

Originally Posted by khylenb
hi,

Iam new to this forum so hope u peolpe can help. I am in my first year of a 4 yr university course training to be a primary/elementary school teacher.

I have beeen given the statement.. 'there are an infinite number of regular polyhedra'

The statment is said by an 8 yr old child. My task is to identify what is wrong with the statement, and how i would explain to the child the correct statement/ what i could show to the child to make them realise this statement is wrong, ansd the correct course of action to put them on th e right track.

I have been told by my maths teacher the statement is incorrect, but that is all the information i have been given, i dont even know what a rugular polyhedra is!!!

Hope sumone on this forum can help???

Thanks

Consider a vertex of a regular polyhedron. There will be a meeting of internal angles of some regular polygons. What number can the angle at this vertex not exceed? When you think about this you should soon see that there can only be a finite number of regular polyhedra.
• Jul 27th 2009, 05:21 AM
Wilmer
A couple of suggestions:

1: drop the chat board lingo (u for you, sum for some ...); you're in university

2: start using Google for questions like you just posted: