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So, all ten listed conditions are at the same time both properties and signs of a ravnogranny tetrahedron. To bring a ravnogrannost out of any condition, it is necessary to build the whole chain of intermediate conditions, in which everyone the subsequent – a direct consequence previous.

The roof has a pyramid form with the square basis of 4,5 m × 4,5 m and a side tilt angle to the basis in 45 ˚. How many sheets of iron of 70 cm × 140 cm in size are necessary for a roof covering if on waste it is necessary to add 10% of the area of a roof?

At turn round direct OS on 360 /5 regular polygon of ABCDE every time will be combined with itself, then the pyramid will be combined with itself also. Means, the straight line on which height of the regular n-coal pyramid lies, is its axis of symmetry of n-go of an order.

As a triangle – the elementary polygon, so a tetrahedron, or a triangular pyramid – the elementary polyhedron. The tetrahedron geometry is not less rich at all, than geometry of his flat colleague – a triangle which many properties we find in the changed look at a tetrahedron. The tetrahedron with a quadrangle – after all at both on four tops has much general.

Pyramids, despite the antiquity, can teach much us. Pyramids with use of the latest devices Americans, Japanese researched. Pyramids were removed from satellites. The American station "Mariner"' transferred photos from Mars in which the same pyramids are represented that suggests an idea of their extraterrestrial origin. So such pyramids?

All pyramids are precisely oriented on parts of the world that testifies to the high level of astronomical knowledge of ancient Egyptians, calculation of tilt angles of sides is absolutely perfect. In pyramid of Cheops a tilt angle such is that height of a pyramid is equal to the radius of the imagined circle in which the pyramid basis is entered.

The polyhedron which consists of a flat polygon, – the bases of a pyramid, the point which is not lying in the basis plane – tops of a pyramid and all pieces connecting pyramid top to basis points is called as a pyramid.

Some of these properties are so obvious that at first sight do not even deserve a mention. Another is remarkable: all these properties are equivalent each other and each of them separately provides a tetrahedron ravnogrannost. Most of all impresses property 10: For equality of sides of a tetrahedron it is enough that their areas were equal among themselves!

Obviously, at a regular pyramid lateral edges are equal; therefore, lateral sides – equal isosceles triangles. Height of a lateral side of a regular pyramid which is carried out from its top is called as an apothem.

The perpendicular which is carried out from any point of one basis on the plane of other basis is called as height of the truncated pyramid. Section the plane passing through two lateral edges of the truncated pyramid which are not lying in one side is called diagonal.