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प्रश्न
Check whether a polyhedron can have V = 12, E = 6 and F = 8.
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उत्तर
By using Euler’s formula for polyhedron,
F + V – E = 2 ...[Where, F = faces, V = vertices, E = edges]
⇒ 8 + 12 – 6 = 2
⇒ 20 – 6 = 2
⇒ 14 ≠ 2
∴ Given values do not satisfy the Euler’s formula. It mean this type of polyhedron cannot be possible.
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संबंधित प्रश्न
Which of the following cannot be true for a polyhedron?
If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.
Complete the table given below:
| S.No | Solid | Shape of Solid |
Number of faces F |
Number of Verticles V |
Number of edges E |
F + V | E + 2 |
| a. | Cuboid |  |
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| b. | Triangular Pyramid |
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| c. | Square Pyramid |
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| d. | Rectangular Pyramid |
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| e. | Pentagonal Pyramid |
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| f. | Hexagonal Pyramid |
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| g. | Triangular Prism |
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| h. | Square Prism |
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| i. | Cube |  |
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| j. | Pentagonal Prism |
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| k. | Octagonal Prism |
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| l. | Heptagonal Prism |
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| Faces | 6 |
| Vertices | q |
| Edges | 12 |
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A polyhedron has 60 edges and 40 vertices. Find the number of its faces.
A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.
