Hint: Break up the icosahedron into twenty congruent triangular pyramids. The height of each pyramid can be found by examining a cross-section of the icosahedron.
back to Regular Polyhedra Project Hints
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What is the radius of a sphere circumscribed around a cube?
Hint: Consider a triangle defined by two segments: that from center of the cube to a vertex and another from the center of the cube to the center of a face touching that vertex.
What is the height of the regular tetrahedron?
Hint: Consider the right triangle formed by the height and a side.
What is the volume of the regular tetrahedron?
Hint: The volume of a pyramid is h A / 3, where h is the height and A is the area of the base.
What is the volume of the regular octahedron?
Hint: Break the octahedron into smaller pieces.
What is the volume of the regular icosahedron?
Hint: Break up the icosahedron into twenty congruent triangular pyramids. The height of each pyramid can be found by examining a cross-section of the icosahedron.
What is the volume of the regular dodecahedron?
Hint: Break up the dodecahedron into a cube and six congruent pieces as shown.