Five Polar Polyhedra

Most polyhedra I post have cuboctahedral, tetrahedral, or icosidodecahedral symmetry, or some pyritohedral or chiral variation of one of these symmetry-types. These, however, are exceptions. I call them “polar polyhedra” because they each have an identifiable “North Pole” and “South Pole,” which are, in three of these five images, at the ends of their axes of rotation.

cub isomorph polar and chiral Compound of enantiomorphic pair

polar and chiral cubic isomorpth

Dual Morph 50.0%

polar polyhedrarhombus-elongated trapezohedron with n = 4

These rotating images were created using Stella 4d, software you may try for yourself, right here.

Basic Trigonometric Functions, Viewed On a Polar Coordinate System


Basic Trigonometric Functions, Viewed On a Polar Coordinate System

The last post made me curious about other trigonometric functions’ graphs, in a polar coordinate system. They were not what I expected. Here they are.

When A Sine Wave Is a Circle


When A Sine Wave Is a Circle

When y=sin(x) is plotted on a polar coordinate system, with everything set, consistently, to radians, the resulting graph is a circle sitting atop the origin, with unit diameter.