Routes On Polyhedra

The first 200 words of this essay...

Routes On Polyhedra

My objective is to find out a rule for how a number of routes change on a polyhedra as the number of edges on the bottom face of the shape changes.

Cuboid

For this cuboid shape,I would have to find

All the routes from the * at A to the . at G.

My method for the cuboid in the diagram

above is to start at A (*) and then find all

the routes that began A-B, then all the routes

that began A-D and finally A-E. I came up

with 16 different routes.

Triangular Prism

I am going to show you all the routes that the triangular prism has within it.

I start with the A to B combinations and the

The A to C and finally A-E

No of edges on the bottom face

Number of rout

3

11/12

4

15/16

5

19/20

6

23/24

These prism polyhedra's fit the rule 4n or 4n-1 because N=No. of edges on bottom face.

= 4 X number of edges on