VIII. Put the words in the correct order to make the sentences.

1. were, ancient, solids, known, Greeks, these, to.

2. meeting, points, are, the vertex, two, there, at.

3. a figure, formed, a polygon, three or more, is, by, points.

4. figure, is, three-dimensional, this, a, geometric.

5. an angle, one quarter, turn, right angle, equal to, compete, is, a, of, a.

6. the eccentricity, the conic, of, the constant, is.

7. central conics, the hyperbola, known, and, are, the ellipse, as.

8. by, a, three, is, a triangle, figure, line, formed, closed, plane, seg­ments.

IX. Give the English equivalents of the following words and word combinations:

многогранный угол, замкнутая пространственная фигура, тело геометрически правильной формы, прямая призма, архимедово тело, кубооктаэдр, грань (плоская поверхность), антипризма, икосододекаэдр, ребро, усеченный куб, полуправильный многогранник, платоново тело восьмигранник (октаэдр), куб, четырехгранник (тетраэдр), выпуклый многогранник, вогнутый многогранник, двадцатигранник (икосаэдр), од­нородный многогранник.

X. Read and decide which of the statements are true and which are false. Change the sentences so they are true.

1. A polyhedron is a surface composed of plane triangular surfaces.

2. The sides of the polygons, joining two faces, are its edges.

3. There're two types of polyhedra: concave and convex ones.

4. The faces of a regular polyhedron are formed by identical (congruent) regular polygons.

5. A tetrahedron has got six square faces.

6. An octahedron has got eight triangular faces.

7. A dodecahedron has got twenty triangular faces.

8. The five regular solids were known to Plato and so they're often
called Platonic solids.

9. A uniform polyhedron is a polyhedron that has identical polyhedral
angles at all its vertices and has all its faces formed by regular polygons.

10. An icosidodecahedron, a cuboctahedron and truncated cube represent the so called "semiregular polyhedra".

XI. Match the terms from the left column and the definitions

from the right column:

congruent	a solid figure with twenty plane surfaces
cube	a solid figure with eight plane surfaces
dodecahedron	a plane figure with five angles and five sides
icosahedron	a solid figure, esp. one with more than six plane surfaces
identical	a solid figure whose ends are parallel, polygonal, and equal in size and shape, and whose sides are parallelograms
octahedron	a solid figure with four triangular faces
pentagon	a solid figure with twelve plane faces
polyhedron	1. a) cut off or replaced by a plane face (said of the angles or edges of a crystal or solid figure), b) having its angles or edges cut off or replaced in this way (said of the crystal or solid figure); 2. having a vertex cut off by a plane that is not parallel to the base(said of a cone or pyramid).
prism	of figures, having identical shape and size
tetrahedron	a solid with six equal, square sides
truncated	1. the very same; 2. exactly alike or equal;

XII. Read the definitions and decide what terms are defined.

a) A solid figure that has four triangular faces.

b) One of the plane regions bounding a polyhedron.

c) A solid figure that has six identical faces.

d) A line joining two vertices of a geometric figure.

e) A polyhedron that has eight faces.

f) A polyhedron that has twelve pentagonal faces.

XIII. Translate the text into English.

МНОГОГРАННИК

Многогранником называется тело, ограниченное конечным числом плоскостей. Это значит, что вся его поверхность расположена в конечном числе плоскостей. Многогранник называется выпуклым, если он лежит по одну сторону каждой из ограничивающих его плоскостей. Общая часть поверхности выпуклого многогранника и ограничивающей его плоскости называется гранью. Стороны граней называются ребрами многогранника, а вершины - вершинами многогранника.

Поясним данное определение на примере куба. Куб есть выпуклый многогранник. Его поверхность состоит из шести квадратов: ABCD, BEFC, ... Они являются его гранями. Ребрами куба являются стороны этих квадратов; АВ, ВС, BE, ... . Вершинами куба являются вершины квадратов А, В, С, D, Е,... . У куба шесть граней, двенадцать ребер и во­семь вершин.

XIV. Read and translate the following sentences. Write 2-3 special and tag questions to each of them:

1. The given figure is formed from two congruent polygons with their
corresponding sides parallel and the parallelograms formed by joining the cor­responding vertices of the polygons.

2. A right prism is one in which the lateral edges are at right angles to
the bases.

3. One base is displaced with respect to the other, but remains parallel to it.

4. The term "cone" is often used loosely for "conical surface".

5. The common vertex isn't coplanar with the base.

6. The pyramid which has its axis perpendicular to its base is a right pyramid.

7. The given surface is composed of plane polygonal surfaces.

8. This term is used for closed solid figures.

9. Greeks thought that these figures played a significant part in geometry.

10. That polyhedron has identical polyhedral angles.

11. Other polyhedra can be generated by truncated the other regular
polyhedron.

12. Kepler used these solids in his complicated model.

13. These solids were already known to Plato.

14. The given plane cuts other faces.

15. We see that all vertices lie at the centers of the edges of the original cube.