नीचे दिए गए त्रिविमीय चित्र पर विचार कीजिए :
उपर्युक्त चित्र में कितने त्रिभुज हैं?
Read this question in English
Consider the following three-dimensional figure:
How many triangles does the above figure have?
(a) 18 · (b) 20 · (c) 22 · (d) 24
उत्तर और व्याख्या · explanation in English
Answer: (b) 20
The solid is a regular icosahedron, and every one of its faces is a triangle. Its edges close into no triangles other than the faces, so the count is simply the number of faces: 20.
- Identify the solid: every face is a triangle and five faces meet at each vertex — a regular icosahedron.
- Count the faces in three layers: 5 around the top vertex, 5 around the bottom vertex and a band of 10 in the middle.
- 5 + 10 + 5 = 20 triangular faces.
- No three edges outside a face close into a triangle, so there are no extra triangles to add.
- Check: Euler's formula V − E + F = 2 with 12 vertices and 30 edges gives F = 20.
Remember · For a solid made of triangular faces, count faces layer by layer and confirm with Euler's formula V − E + F = 2.
Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 1 Oct 2026 (how we verify). ·