Geometry of Polyhedrons by 'Literka'.

List of pages.

1. Plato's polyhedrons (regular polyhedrons).
1. Icosahedron - regular polyhedron with 20 faces.
2. How to build a regular dodecahedron. All you need is 12 (unusable for computer) CD-ROM disks.
3. How to compute volume of a regular dodecahedron. Given lengths of its edges.
4. How to compute volume of a regular icosahedron.
2. Convex polyhedrons built of equilateral triangles.
1. Polyhedron built of 16 equilateral triangles.
3. Convex polyhedrons built of rhombuses.
1. Polyhedron built of 30 equal rhombuses.
2. How to compute volume of a polyhedron built of 30 congruent rhombuses. Given lengths of its edges.
3. Few remarks on polyhedrons built of rhombuses.
4. Antiprisms. Volume formula.
5. Semi-regular polyhedrons (built of regular polygons).
   1. Four examples of semi-regular polyhedrons.
      1. Example of a semi-regular polyhedron of 62 faces.
   2. Example of a semi-regular polyhedron of 32 faces built of regular hexagons and pentagons.
   3. Semi-regular polyhedrons built of congruent regular polygons and equilateral triangles.
6. Polyhedron of a soccer ball used by UEFA for European Soccer Competitions.
7. Pyramids, theirs cross sections similar to ellipses.
1. Related topic: Ellipse as planet's trajectory.
   1. Applet - planet's motion, radius vector, Keppler's law.
8. FAQ - Frequently asked questions.

New feature of a program Ruler and Compass version 1.7. New module "Cubic Functions" showing roots of cubic equations. Newly written calculator, which can give results with up to 900 significant digits. Version 1.7 allows complex numbers. New feature of version 1.7 - "Curves".				See a page of 'Literka' Geometry of Polytopes for a complete list of pages related to polytopes. Some links are listed below.
See the list and descriptions of mathematical pages. MATHEMATICAL COUNTRYSIDE remote pages: Monotonic subsequences. Roots of cubic equation. Cardano's formula. Positive random walks. Rudin's Theorem of Complex Analysis. Exact values of trigonometric functions of angles 2*k*pi/11. Exact values of trigonometric functions of angles 2*k*pi/13. Exact values of cos(2*k*pi/17). Exact values of trigonometric functions of angles (n*pi)/17. Equalities for values of trigonometric functions of angles (n*pi)/17. Factorization of a polynomial, which defines values of sine function (angles n*pi/17). Polynomials with roots cos(2*k*pi/n). Factorization of polynomials with roots cos(2*k*pi/n), where n is Fermat number. Values of trigonometric functions of angles (n*pi)/257. Part I. Values of trigonometric functions of angles (n*pi)/257. Part II, Part III, Part IV, Part V, Part VI, Part VII. Values of trigonometric functions of angles (n*pi)/65537. Part I. Values of trigonometric functions of angles (n*pi)/65537. Part II, Part III, Part IV and Part V, Part VI, Part VII, Part VIII, Part IX, Part X, Part XI, Part XII, Part XIII, Part XIV. An elementary problem can be unsolvable. A Remarkable Monotonic Property of the Gamma Function . Weight centers of simple geometrical figures. Weierstrass Approximation Theorem. Bernstein's Polynomials. Construction of a regular pentagon. Construction of a regular heptadecagon. Construction of a regular polygon with 257 sides.				Visit our new FORUM of Literka and post a message there (related to mathematics). Click here.

List of polytopes pages.

1. Nets of regular polytopes.
   1. Nets of 5-cells and 8-cells regular polytopes.
   2. Nets of 16-cells and 24-cells regular polytopes.
2. Cross sections of regular polytopes.
   1. Cross sections of a regular 4-dimensional hypercube.
   2. Cross sections of a 16-cells regular polytope.
   3. Cross sections of a 24-cells regular polytope.
      1. Applet: Cross sections of regular 24-cells polytope.
         
      2. Applet: Cross sections of a regular 600-cells polytope.
   4. Example of a 42-faces polyhedron - cross section of a 4-dimensional 120-cells regular polytope.
   5. Cross sections of a 600-cells regular polytope.
3. Polytopes built of congruent bipyramids.
   1. Four examples of polytopes built of congruent bipyramids.
      1. Applet: Cross sections of 2 polytopes built of congruent bipyramids (24 and 32 cells).
      2. Applet: Cross sections of polytopes built of congruent bipyramids (96 cells).
   2. Two examples of polytopes built of congruent bipyramids.
      1. Applet: Cross sections of 2 polytopes built of congruent bipyramids (720 and 1200 cells).

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