We think you are located in United States. Is this correct?

Chapter summary

Test yourself now

High marks in science are the key to your success and future plans. Test yourself and learn more on Siyavula Practice.

Sign up and test yourself

25.7 Chapter summary

  • Regular polygons are polygons that have all sides equal and all interior angles equal.
  • A face is any flat surface on a 3D object.
  • An edge is the line segment along which two faces of a 3D object join together.
  • A vertex is the corner or point where edges of a 3D object meet.
  • The Platonic solids are a special group of 3D objects with faces that are congruent regular polygons.
    • A tetrahedron is an object with four congruent triangular faces.
    • A hexahedron (cube) is an object with six congruent square faces.
    • An octahedron is an object with eight congruent triangular faces.
    • A dodecahedron is an object with twelve congruent pentagonal faces.
    • An icosahedron is an object with twenty congruent triangular faces.
  • Euler’s formula states that the difference between the number of vertices (\(v\)) and the number of edges (\(e\)) added to the number of faces (\(f\)) is equal to \(2\): \(v - e + f = 2\)
  • General properties of the five Platonic solids:
    • All faces are regular and congruent.
    • The same number of faces meet at each vertex.
    • All the edges are the same length.
    • Euler’s formula is satisfied.
  • A net is a flat diagram that can be folded to form a three-dimensional shape.
  • A pyramid is an object that has a polygon as its base and triangular sides that converge at an apex.
  • The apex is the highest point of an object and it is usually the vertex opposite the base.