X-Nico

4 unusual facts about Polyhedron


Euclidean shortest path

The Euclidean shortest path problem is a problem in computational geometry: given a set of polyhedral obstacles in a Euclidean space, and two points, find the shortest path between the points that does not intersect any of the obstacles.

Mysterium Cosmographicum

This book explains Kepler's cosmological theory, based on the Copernican system, in which the five Pythagorean regular polyhedra dictate the structure of the universe and reflect God's plan through geometry.

Ourmiavirus

Virions are encapsulated, non-enveloped, elongated and shows polyhedral symmetry with a length of 26–76 nm and a width of 18–26 nm.

Ped

In the granular structure, the structural units are approximately spherical or polyhedral and are bounded by curved or very irregular faces that are not casts of adjoining peds.


Chamfered cube

This polyhedron is also a part of a sequence of truncated rhombic polyhedra and tilings with n,3 Coxeter group symmetry.

Császár polyhedron

The Császár polyhedron is named after Hungarian topologist Ákos Császár, who discovered it in 1949.

Cyndor

The exact relationship between Cyndor and the Suel time-god Lendor is unknown, though Lendor has been referred to as Cyndor's "sometime ally (and superior)." Polyhedron #140 states that Lendor is sometimes his ally and sometimes his foe.

Electron counting

Polyhedral skeletal electron pair theory for cluster compounds, including transition metals and main group elements such as boron including Wade's rules for polyhedral cluster compounds, including transition metals and main group elements and mixtures thereof.

Proofs and Refutations

The book is written as a series of Socratic dialogues involving a group of students who debate the proof of the Euler characteristic defined for the polyhedron.

Rhombic icosahedron

A rhombic icosahedron (or rhombic icosacontahedron) is a polyhedron shaped like an oblate sphere.

Rhombic triacontahedron

This polyhedron is a part of a sequence of rhombic polyhedra and tilings with n,3 Coxeter group symmetry.

Rhombicuboctahedron

The large polyhedron in the 1495 portrait of Luca Pacioli, traditionally though controversially attributed to Jacopo de' Barbari, is a glass rhombicuboctahedron half-filled with water.

Semiregular polyhedron

In its original definition, it is a polyhedron with regular faces and a symmetry group which is transitive on its vertices, which is more commonly referred to today as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general semiregular polytope).


see also