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Three-dimensional solids and Euler’s formula
Prisms, pyramids and other polyhedra, counting faces, vertices and edges, and Euler's formula F + V − E = 2.
Polyhedra
A polyhedron is a solid with flat faces. A prism has two identical, parallel ends joined by rectangles; it is named after its end (triangular prism, hexagonal prism). A pyramid has one base and triangular faces meeting at an apex.
Euler's formula
It works for every convex polyhedron. Check a cube: $6 + 8 - 12 = 2$.
A polyhedron has $12$ vertices and $30$ edges. How many faces does it have?
A polyhedron has $12$ vertices and $30$ edges. How many faces?
$F = 2 - 12 + 30$.
How many edges does a pentagonal prism have?
$3 \times 5$.
How many faces does a square-based pyramid have?
$4 + 1$.
How many edges does a hexagonal pyramid have?
$2 \times 6$.
How many vertices does a triangular prism have?
$2 \times 3$.
Which is not a polyhedron?
A cone has a curved surface.
A polyhedron has $6$ faces and $12$ edges. How many vertices?
$V = 2 - 6 + 12$.
A prism has $24$ edges. How many sides does its base have?
$3n = 24$.
New numbers every time. Keep going until you get five in a row.