Solid figures and polyhedra
A solid bounded by plane polygons is a polyhedron; the polygons are its faces, their sides are the edges and their vertices are the vertices of the polyhedron. A segment joining two vertices not on one face is a diagonal. A polyhedron is convex if it lies on one side of the plane of each of its faces (for example the cube). A prism has two faces (the bases) that are equal polygons and the other faces (lateral faces) are parallelograms; if the lateral faces are perpendicular to the base the prism is right, otherwise oblique, a right prism on a regular polygon is regular; a prism whose base is a parallelogram is a parallelepiped, a right one with a rectangular base is a rectangular parallelepiped, and if all dimensions are equal it is a cube. A pyramid has one face (the base) a polygon and the other lateral faces triangles with a common vertex; if the base is a regular polygon and the height passes through its centre, the pyramid is regular, and the altitude of a lateral face drawn from the apex is the apothem. In a regular pyramid the lateral edges, lateral faces and apothems are equal, and the lateral surface is S = p · a (p — semi-perimeter of the base, a — apothem).
In class build models of a cube, a triangular prism and a quadrilateral pyramid from card, sticks and modelling clay (an adult handles scissors and knives); count the vertices, edges and faces of each model and fill in a table.