Holyhedron
Encyclopedia
In mathematics
, a holyhedron is a type of 3-dimensional geometric
body: a polyhedron
each of whose faces contains at least one polygon
-shaped hole, and whose holes' boundaries share no point with each other or the face's boundary.
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, divided by the number of faces for finding an example, asking:
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 prize money.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a holyhedron is a type of 3-dimensional geometric
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
body: a polyhedron
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
each of whose faces contains at least one polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
-shaped hole, and whose holes' boundaries share no point with each other or the face's boundary.
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, 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 connectedConnected spaceIn topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets. Connectedness is one of the principal topological properties that is used to distinguish topological spaces...
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 prize money.