Worked Example 1
Count the faces, vertices and edges of a triangular prism, and check with Euler's formula.
FacesTwo triangular ends and three rectangles: F = 5.
VerticesThree at the front and three at the back: V = 6.
EdgesThree front, three back, three joining: E = 9.
Check5 + 6 - 9 = 2. Correct.
Worked Example 2
A hexagonal pyramid: work out all three counts without holding one.
Reason it outA pyramid is a base pulled up to one point. The base is a hexagon: 6 sides, 6 corners.
FacesF = 1 + 6 = 7.
VerticesV = 6 + 1 = 7.
EdgesE = 6 + 6 = 12.
Check7 + 7 - 12 = 2. For any pyramid, faces and vertices are always equal.
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