Euler's Formula

Questions based on Euler's Formula worksheet covering vertices, faces, edges, and calculations using Euler's Theorem.

What is the formula by which the number of vertices (V), edges (E), and faces (F) of a polyhedron are related?

Euler's formula, which states that V + F = E + 2.

If a polyhedron has 6 faces and 7 vertices, how many edges does it have?

It has 11 edges, calculated using Euler's formula: 6 + 7 - 2 = 11.

How many edges are there in a polyhedron with 9 faces and 21 edges?

It has 21 edges as stated in the problem, but the number of vertices can be calculated using Euler's formula.

Using Euler's Theorem, calculate the vertices of a polyhedron with 12 faces and 30 edges.

The polyhedron has 20 vertices.

How many faces does a polyhedron with 6 edges and 4 vertices have according to Euler's Theorem?

The polyhedron has 4 faces.

What is the relationship between the number of edges, vertices, and faces in a square pyramid?

In a square pyramid: F = n+1, V = n+1, E = 2n where n is the number of sides in the base.

If a polyhedron has 6 faces and 8 vertices, how many edges does it have?

It has 12 edges, calculated using Euler's formula: 6 + 8 - 2 = 12.

What is the number of vertices for a triangular prism?

For a triangular prism, the number of vertices is 6.

How many edges does a pentagonal pyramid have?

A pentagonal pyramid has 10 edges.

What is the face-vertex-edge relation for a cube?

A cube has 6 faces, 8 vertices, and 12 edges.