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.


A circle with a diameter of

can be constructed by drawing the line that satisfies




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".

See also

Zeroth First Second Third Fourth Fifth Sixth Seventh Eighth Ninth Tenth Eleventh Twelfth Thirteenth Fourteenth Fifteenth Sixteenth
Simplex Point Line Triangle Tetrahedron Pentachoron Hexateron Heptapeton Octaexon Enneazetton Decayotton Hendecaxennon Dodecadakon Tredecahendakon Quattuordecadokon Quindecatradakon Sexdecateradakon Septendecapetadakon
Hypercube Point Line Square Cube Tesseract Penteract Hexeract Hepteract Octeract Enneract Dekeract Undekeract Dodekeract Tredekeract Quattuordekeract Quindekeract Sexdekeract
Cross Point Line Square Octahedron Hexadecachoron Pentarss Hexarss Heptarss Octarss Ennearss Decarss Hendecarss Dodecarss Tredecarss Quattuordecarss Quindecatrarss Sexdecaterarss
Hypersphere Point Line Circle Sphere Glome Hyperglome Hexaphere Heptaphere Octaphere Enneaphere Decaphere Hendecaphere Dodecaphere Tredecaphere Quattuordecaphere Quindecatraphere Sexdecateraphere
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