Given a regular tetrahedron with volume and a cube with volume , which object has smaller surface area?
Details and Assumptions:
In a regular tetrahedron, all four faces are equilateral triangles, and
In a cube, all six faces are squares.
The perfect slice through a cube will reveal a regular hexagonal cross section. If this is a cube, what is the surface area of the hexagonal cross section?
The dodecahedron has 12 pentagonal faces. Therefore it has edges.
The icosahedron has 20 equilateral triangular faces. Therefore it has edges.
How many edges does a truncated icosahedron have?
After drawing in the diagonal perforations onto a unit cube, we are left with a geometric shape object. What is the volume of this new object?
A solid has 12 faces and 20 edges. Given that Euler's Formula applies, how many vertices does it have?