Polyhedrons - class-VIII

Solid figures with line segments as their edges are called  Polyhedrons

Solid figures having only line segments as their edges are called polyhedrons.

A sphere is defined as the set of points at a fixed distance from a center, forming a single continuous curved surface.

A tetrahedron is a triangular pyramid, which has 4 triangular faces, 4 vertices, and 6 edges.

A tetrahedron is a polyhedron with exactly 4 triangular faces.

A polyhedron must be a closed 3D solid. At least 4 faces are required to enclose a volume in 3D space.

A sphere is a perfectly round geometrical object in 3D space where all points on the surface are equidistant from the center and has no vertices or edges.

Euler's formula for polyhedra is V - E + F = 2. For F = 10, E = 20, V = 15: 15 - 20 + 10 = 5. Since 5 is not equal to 2, such a polyhedron cannot exist.

A cube is a regular polyhedron because all its faces are congruent regular polygons (squares) and the same number of faces meet at each vertex. A cuboid is not regular because its faces are not necessarily congruent squares.

Both a cube and a cuboid have 6 faces, 12 edges, and 8 vertices.

Cone is not a polyhedron as it has a curved surface. Similarly cylinder also not a polyhedron.

It is possible, only if the number of faces are greater than or equal to 4

In a tetrahedron OABC with OA=OB=OC=K and equal face angles theta at O, the dihedral angles and face angles are constrained by the geometry of the solid. The range of the face angle theta for such a tetrahedron is [pi/3, 2pi/3].