How many edges does a solid regular octahedron have?
A regular octahedron has 6 vertices, 8 triangular faces, and 12 edges (satisfies Euler's formula V - E + $F = 6 - 12 + 8 = 2$).
How many vertices does a solid regular dodecahedron have?
A regular dodecahedron has 12 pentagonal faces, 30 edges, and 20 vertices (V - E + $F = 20 - 30 + 12 = 2$).
Which transformations are 2D isometries that preserve lengths, angles, and area?
Translations, rotations, and reflections are isometries. Scaling by a factor other than 1 changes lengths and area.
A paper rectangle of size 10 cm x 5 cm is rolled along its longer edge (10 cm) to form a open cylinder without overlap. What is the height of the resulting cylinder?
Rolling along the 10 cm edge makes 10 cm the circumference of the circular base, so the shorter edge (5 cm) forms the height of the cylinder.
When a solid cone is cut by a plane parallel to its base, the lower remaining portion containing the base is called a:
Cutting a cone parallel to its base yields a smaller top cone and a bottom section known as a frustum.