# Regular solids

Not what you're looking for?

For each of the 5 regular polyhedra, enumerate the number of vertices (v), edges (e), and faces (f), and then evaluate the quantity v - e + f. (One of the most interesting theorems relating to any convex polyhedron is that v - e + f = 2. -> This was given as part of the problem. I am not sure if it is of any value when solving this problem or not.)

Please use pictures to illustrate the concept above along with a detailed explanation of your response. Thank you.

##### Purchase this Solution

##### Solution Summary

This shows how to find the number of vertices (v), edges (e), and faces (f) of polyhedra.

##### Solution Preview

See attachment please!

A polyhedron is a 3-dimensional closed figure made from flat sides, or 'faces'. There are an infinite number of them. A barn, for example, has many flat surfaces or faces; it's a polyhedron. So it a textbook. A prism. The diamond in a ring. All these figures are made from flat 'faces'.

But on each one of the objects mentioned above , some of the faces are different shapes. Is there a polyhedron with all the faces the same?

Yes there is. In fact, there are just five of them! You are familiar with at least one of them ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Probability Quiz

Some questions on probability

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.