Question

1) write the Euler's formula=_______?
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Answer 1

Euler's formula

In all the polyhedrons, such as prisms, pyramid, platonic solids and other solids with two shapes that we see, there is a relationship between their faces, vertices, edges.

Now exploring Euler's formula:-

$(f + v) - e = 2$

Cube:-

Faces= 6

Vertices= 8

Edges= 12

(F+V)-E=2

(6+8)-12=2

14-12=2

Yes, it holds Euler's formula.

Triangular prism:-

Faces= 5

Vertices= 6

Edges= 9

(F+V)-E=2

(5+6)-9=2

11-9=2

Yes, it holds Euler's formula.

Square pyramid:-

Faces= 5

Vertices= 5

Edges= 8

(F+V)-E=2

(5+5)-8=2

10-8=2

Yes, it holds Euler's formula.

Hexagonal prism:-

Faces= 8

Vertices= 12

Edges= 18

(F+V)-E=2

(8+12)-18=2

20-18=2

Yes, it holds Euler's formula.

Traingular prism:-

Faces= 4

Vertices= 4

Edges= 6

(F+V)-E=2

(4+4)-6=2

8-6=2

Yes, it holds Euler's formula

Octahedron:-

Faces= 8

Vertices= 6

Edges= 12

(F+V)-E=2

(8+6)-12=2

14-12=2

Yes, it holds Euler's formula

Nested solid:-

Faces= 9

Vertices= 9

Edges= 16

(F+V)-E=2

(9+9)-16=2

18-16=2

Yes, it holds Euler's formula

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