Polyhedrons Presentation shows how origami can be used for introducing students with the notion of polyhedrons

Definitions Dihedron: The figure formed by two intersecting planes and the line in which they meet A dihedron can be considered a degenerate prism consisting of two (planar) n-sided polygons connected "back-to-back", so that the resulting object has no depth.

Sum of angles in convex solid angle is less than 360° Рогаљ

Exercise It is given an dihedron and a line that interests both sides of dihedron. The line is perpendicular to one side. If a part of a line between to sides is 6cm, and distance between line and perpendicular dihedron edge is 8cm, calculate the distance between the line and dihedron edge on the other side. Two planes intersect in 60 degrees. If the point A on one plane is on 4cm distance from intersect line, and point B on second plane is on 3cm distance from intersect line, calculate distance between points.

Surface of polihedron Polyhedrons` surface is a union of a finite set of polygons that meet the following requirements: For every two nonadjacent polygons M and M’ from set polygons M, M1, M2, ..., Mn, M’ made of polygons of that set, so that every two consecutive polygons in the series are not neighbored. . Joint border of every two consecutive edges of polygons and is not border of any other polygons. Two nonadjacent polygons, either with no section or with cross-section of a common vertices for these two polygons.

Theorems Number of edge angles are twice of number of edges. Sum of edge angles of a convex polyhedron, with t numbers of vertices is: S=(t-2)·360° Eulers theorem t+s=i+2, t number of vertices, s number sides, I number of edges in convex polyhedron.

Making geometrical solids such as: cube, tetrahedron, etc we can see what does vertices or sides of polyhedrons means.

Make it by origami techniques Make it by origami techniques. Browse the notion of convexity and concavity of polyhedrons.

Make a solid by origami. First stem is sonobe piece. Follow the steps:

Make a dihedron by the sonobe pieces. Make a solid angle by tree sonobe pieces. Make a cube. Make star like polyhedron. Explore

Number of sonobe pieces Model Number of sonobe pieces Tetrahedron 3 Small cube 6 Big cube 12 Star like octahedron Star like icosahedrons 30