Question

find the solution using euler's formula (2) Can a polyhedron have 20 Faces, 30 Edges and 12 Vertices? Prove by Euler’s formula.​

Answer 1

Answer:

Methodology. Euler's method uses the simple formula, to construct the tangent at the point x and obtain the value of y(x+h) , whose slope is, In Euler's method, you can approximate the curve of the solution by the tangent in each interval (that is, by a sequence of short line segments), at steps of h .

In euler's method, with the steps, you can say for example, if step is 0.5 (or Delta X, i.e change in x is 0.5), you will have: dy/dx is given thanks to differential equation and initial condition. You just plug it in and get a value. y1 is the y value at which the slope is the dy/dx and y2 is the y you're looking for.

Answer 2

Solution:-

Eulers Formula For A Polyhedron,

= V(Vertices)- E(Edges)+ F (faces)= 2

Here,

• F = 20
• V = 12
• E = 30

Thus,

$12 - 30 + 20 = 2 ,$

Which satisfy The Euler's Formula.

Hence, a Polyhedron Can Have 20 faces , 12 Vertices and 30 edges.

Answer :- Yes