Question

verify Euler's forumula for, faces=12,vertices=20 and edges =30​

Answer 1

Step-by-step explanation:

Euler's formula is No.of Faces(F) + No. of vertices(V) - No. of edges(E) = 2

That is: F + V - E = 2

In this case, substituting the values:

LHS : 12 + 20 - 30 => 32 - 30 = 2 = RHS

Since LHS = RHS, it is valid

Hence Proved.

Answer 2

Answer:

$2$

Step-by-step explanation:

Euler's formula is given by $F+V-E=2$

$F=12, V=20, E=30$

$F+V-E=12+20-30=32-30=2$

$\therefore$ Euler's formula is satisfied.

Euler's formula:

One of Leonhard Euler's two key mathematical theorems is the formula. The first equation, often known as the Euler identity and utilised in trigonometry, reads: eix = cos x + isin x, where e is the base of the natural logarithm and I is the square root of 1. (see imaginary number). The formula produces two beautiful formulations that relate x, e, and I ei = 1 and e2i = 1, respectively, when x equals 0 or 2. The second is a topological invariance (see topology) that links the quantity of faces, vertices, and edges in any polyhedron. It is also known as the Euler polyhedra formula. F is the number of faces, V is the number of vertices, and E is the number of edges. This equation is represented as F + V = E + 2.

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