Find, with a proof, the variety of vertices, edges, and faces that a dodecahedron.

You are watching: How many vertices does a dodecahedron have

Its is clear that their are $20$ vertices, $30$ edges, and $12$ faces. I am no sure how to prove this though.


For vertices, there are $12$ encounters times $5$ vertices per face but since each confront is associated to $3$ vertices the is counted 3 times. Therefore, $V = 12 imes 5 div 3 = 20$.

For edges, there space $12$ faces times $5$ edge per confront but since each edge joins $2$ encounters it is counted twice. Therefore, $E = 12 imes 5 div 2 = 30$.

Do you watch the pattern? try the same exercise with a tetrahedron and an octahedron to check out if you obtain it.



Thanks because that contributing response to Stack Exchange!

Please be sure to answer the question. Carry out details and share your research!

But avoid

Asking because that help, clarification, or responding to other answers.Making statements based on opinion; ago them increase with recommendations or an individual experience.

Use ubraintv-jp.comJax to format equations. ubraintv-jp.comJax reference.

See more: Why Is Algae Not A Plant - Why Are Algae Considered Plants

To find out more, check out our advice on writing great answers.

article Your price Discard

By click “Post your Answer”, you agree to our terms of service, privacy policy and also cookie plan

Not the answer you're looking for? Browse other questions tagged geometry or questioning your very own question.

What are the formulas for the number of vertices, edges, faces, cells, 4-faces, ..., $n$-faces, that convex continuous polytopes in $n geq 5$ dimensions?
Probability the connecting two vertices in a dodecahedron will result in a segment within the dodecahedron

site design / logo design © 2021 stack Exchange Inc; user contributions licensed under cc by-sa. Rev2021.10.22.40552

ubraintv-jp.comematics stack Exchange works best with JavaScript permitted

her privacy

By click “Accept every cookies”, friend agree ridge Exchange can store cookie on your machine and disclose info in accordance with our Cookie Policy.