Circle



A circle is a rotatope with no flat dimensions and two round dimensions. It is, therefore, the 2D hypersphere. It can also be considered as the set of all points that are the same distance from a point (the center of a circle) in the plane.

In the plane, a circle will roll, as it is completely round. The proof of this is that if you trace the path the middle of a circle takes when it rolls, that that is straight. Circle could not roll on other surfaces smoothly.

Equation
A circle with a diameter of

$$l$$ can be constructed by drawing the line that satisfies

$$2\sqrt { { x }^{ 2 }+{ y }^{ 2 } } ={ l }$$ .

Hypervolumes

 * vertex count =$$N/A$$
 * edge length (circumference) =$$\pi l$$
 * surface area =$$\frac { \pi }{ 4 } { l }^{ 2 }$$

Subfacets
A circle has no zero-dimensional subfacets. Its only one-dimensional subfacet is its edge, which is also, quite confusingly, called a circle. To unambiguously distinguish between the 1D length and the 2D area, the area can be called a "disc".
 * 1 circle (1D)