In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, a holyhedron is a type of 3-
dimensional
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordi ...
geometric
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
body: a
polyhedron
In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal Face (geometry), faces, straight Edge (geometry), edges and sharp corners or Vertex (geometry), vertices. The term "polyhedron" may refer ...
each of whose faces contains at least one
polygon
In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain.
The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...
-shaped hole, and whose holes' boundaries share no point with each other or the face's boundary.
History
The concept was first introduced by
John H. Conway; the term "holyhedron" was coined by
David W. Wilson in 1997 as a pun involving polyhedra and holes. Conway also offered a prize of 10,000
USD
The United States dollar (symbol: $; currency code: USD) is the official currency of the United States and several other countries. The Coinage Act of 1792 introduced the U.S. dollar at par with the Spanish silver dollar, divided it int ...
, divided by the number of faces, for finding an example, asking:
:''Is there a polyhedron in Euclidean three-dimensional space that has only finitely many plane faces, each of which is a closed
connected
Connected may refer to:
Film and television
* ''Connected'' (2008 film), a Hong Kong remake of the American movie ''Cellular''
* '' Connected: An Autoblogography About Love, Death & Technology'', a 2011 documentary film
* ''Connected'' (2015 TV ...
subset of the appropriate plane whose relative interior in that plane is multiply connected?''
No actual holyhedron was constructed until 1999, when Jade P. Vinson presented an example of a holyhedron with a total of 78,585,627 faces;
another example was subsequently given by Don Hatch, who presented a holyhedron with 492 faces in 2003, worth about 20.33
USD
The United States dollar (symbol: $; currency code: USD) is the official currency of the United States and several other countries. The Coinage Act of 1792 introduced the U.S. dollar at par with the Spanish silver dollar, divided it int ...
prize money.
[
]
References
{{reflist
External links
Don Hatch's 492-face holyhedron
Polyhedra
John Horton Conway