Question

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

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Answer 1

No, it can't have 10 faces , 20 edges, and 15 vertices as The formula i.e. Euler's formula isn't being satisfied.

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Answer 2

$\huge{ \mathfrak { \fbox{ \red{ꜱᴏʟᴜᴛɪᴏɴ}}}}$

Given:

• faces = 10,
• Edges = 20,
• Vertices = 15

According to Euler’s Formula:

F + V – E = 2

⇒ 10 + 15 – 20 = 25 – 20

⇒ 5 ≠ 2

∴ A polyhedron do not have 10 Faces, 20 Edges and 15 Vertices.

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