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  ## 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.
explanation: The provided text is an educational excerpt that summarizes key concepts related to geometry, specifically focusing on regular polygons, 3D objects, and Platonic solids. It includes definitions and properties of various geometric shapes and Euler’s formula. The text does not contain a specific question or a question-and-answer pair.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Home Practice
  For learners and parents For teachers and schools
  Textbooks
  Full catalogue
  Pricing Support
  
  We think you are located in United States. Is this correct?
  
  # Test yourself now
  
  High marks in science are the key to your success and future plans. Test yourself and learn more on Siyavula Practice.
  
  ## 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.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is an educational excerpt that summarizes key concepts related to geometry, specifically focusing on regular polygons, 3D objects, and Platonic solids. It includes definitions and properties of various geometric shapes and Euler’s formula. The text does not contain a specific question or a question-and-answer pair.
  
  Label: no-question