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Visualising Solid Shapes

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Visualising Solid Shapes - Lesson Summary

Three dimensional objects or solids generally have length, breadth and height. Three dimensional objects look different from different locations or angles.

A polyhedron is a solid shape bounded by polygons whereas non-polyhedrons do not have polygon shaped faces.

Polygons forming a polyhedron are known as its faces.
Line segments common to intersecting faces of a polyhedron are known as its edges.
Vertices Points of intersection of edges of a polyhedron are known as its vertices.
Reguler polyhedron
A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex.

Irregular polyhedron
An irregular polyhedron is made of polygons whose sides and angles are not of equal measure. Cubes, cuboids, prisms, and pyramids are few examples of polyhedrons. Spheres, cones and cylinders are a few examples of non-polyhedrons.

F + V = E + 2 is known as Euler’s formula and it holds true for any polyhedron. Here F stands for faces, V for vertices and E for the edges of the polyhedron.

Convex polyhedron
In a convex polyhedron, the line segment joining any two points on the surface of the polyhedron lies entirely inside or on the polyhedron.

Concave polyhedron
A polyhedron some of whose plane sections are concave polygons is known as a concave polyhedron. Concave polygons have at least one interior angle greater than 180° and has some of its sides bent inward.

A prism is a polyhedron with parallel congruent polygon bases and sides made of parallelograms.

A pyramid is a polyhedron whose base is a polygon of any number of sides and whose lateral faces are triangles with a common vertex.

Prisms and pyramids are named after the shape of their base.
Maps represent the location of a place or object in relation to other places or objects.


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