Platonic solids provide one storehouse of fundamental ideas1
I define campolyhedron2 as a curved polyhedron3 with curves that are circular arcs. Regular if they have the same angles and radii. Semiregular if they have the same radii. All classical polyhedrons has your correspondent campolyhedron? I think so. Now we will see someone:
There are three types of campolyhedra in the images. Where are the regular icosahedron and dodecahedron campolyhedra? How have I built them?
All classical polyhedrons has your corresponding campolyhedron? I think so. Now we will see someone:
If you want a particular campolyhedron, ask me about it.
Aristotle and the perfection of the circle
Furthermore, this circular notion is necessarily primary. For the perfect is naturally prior to the imperfect, and the circle is something perfect. This cannot be said of the straight line
Aristotle, De Caelo, 269a 19-21
Excellence of the circular movement, its primacy in the hierarchy of movements:
“Clearly circular motion is the primary kind of locomotion. For all locomotion is either circular, rectilinear, or mixed. Now the simple kinds must be prior to the mixed. And the circular kind is prior to the rectilinear; for (1) it is simpler and more perfect. For it is impossible to move along an infinite straight line (since there is not such thing, and if there were it could not be traversed); and motion along a finite one, if it turn back, is really two motions, while if it does not it is imperfect and comes to an end. But the perfect is prior to the imperfect, the imperishable to the perishable, by nature, in definition, and in time.(2) A motion that can be eternal is prior to one that cannot; now circular motion can, and no other locomotion or indeed change can, since it must be interrupted by rest”.
Aristotle’s Physics, W. D. Ross. VIII 265ª 13-24.
1CSE325 Computer Science and Sculpture. Prof. George Hart
2Cam is circular arc math =cam. Also in gaelic is Bend; bent, crooked, object. (Camariñas=Cam a rinn). Also Mathematica has your logo with a curved dodecahedron, a campolyhedron or use a camicosahedron.
3Wikipedia Curved polyhedra (Some fields of study allow polyhedra to have curved faces and edges). Spherical polyhedra. Curved spacefilling polyhedra.
PS. A true camtetrahedron in lines and solid
The first camicosahedron in Roman times. Rheinisches Landes-Museum. Bonn.
You will see the artworks in Bridges 2023, Dalhousie University Halifax, Nova Scotia, Canada, 27–31 July 2023