Mathematics
Can a polyhedron have :
(i) 3 triangles only ?
(ii) 4 triangles only ?
(iii) a square and four triangles?
Answer
(i) No, a polyhedron cannot have only 3 triangles as its faces because a polyhedron must have at least four faces.
(ii) Yes, a polyhedron can have 4 triangles, which is known as a pyramid with a triangular base, because all the edges meet at the vertices.
(iii) Yes, a polyhedron can have a square and four triangles as its faces, forming a pyramid with a square base, because all eight edges meet at the vertices.
Related Questions
Verify Euler's formula for the following three dimensional figures :
(i)
(ii)
(iii)
Can a polyhedron have 8 faces, 26 edges and 16 vertices ?
Using Euler's formula, find the values of x, y and z
S.No Faces Vertices Edges (i) x 15 20 (ii) 6 y 8 (iii) 14 26 z What is the least number of planes that can enclose a solid ? What is the name of the solid ?