Cubic Polyhedra
نویسندگان
چکیده
A cubic polyhedron is a polyhedral surface whose edges are exactly all the edges of the cubic lattice. Every such polyhedron is a discrete minimal surface, and it appears many (but not all) of them can be relaxed to smooth minimal surfaces (under an appropriate smoothing flow, keeping their symmetries). Here we give a complete classification of the cubic polyhedra. Among these are five new infinite uniform polyhedra and an uncountable collection of new infinite semiregular polyhedra. We also consider the somewhat larger class of all discrete minimal surfaces in the cubic lattice.
منابع مشابه
A generalized ring spiral algorithm for coding fullerenes and other cubic polyhedra
The so called ring spiral algorithm is a convenient means for gen erating and representing certain fullerenes and some other cubic poly hedra In Manolopoulos and Fowler presented a fullerene on vertices without a spiral No smaller unspirable fullerene is known In the spring of using computer Gunnar Brinkmann found the smallest cubic polyhedron without a spiral It has only vertices Here we gener...
متن کاملA Generalized Ring Spiral Algorithm for CodingFullerenes and other Cubic Polyhedra 1
The so-called ring spiral algorithm is a convenient means for generating and representing certain fullerenes and some other cubic poly-hedra. In 1993 Manolopoulos and Fowler presented a fullerene on 380 vertices without a spiral. No smaller unspirable fullerene is known. In the spring of 1997, using computer, Gunnar Brinkmann found the smallest cubic polyhedron without a spiral. It has only 18 ...
متن کاملRegular and Chiral Polyhedra in Euclidean Nets
We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose vertex and edge sets are a subset of those of the primitive cubic lattice, the face-centred cubic lattice, or the body-centred cubic lattice.
متن کاملImmobilization of Bioactive Growth Factors into Cubic Proteinous Microcrystals (Cypovirus Polyhedra) and Control of Cell Proliferation and Differentiation
Certain insect viruses produce stable infectious microcrystals called polyhedra which function to protect the virus after the death of infected larvae. Polyhedra form within infected cells and contain numerous virus particles embedded in a crystalline lattice of the viral protein polyhedrin. We have previously demonstrated that the Nterminal 75 amino acids of the Bombx mori cypovirus (BmCPV) tu...
متن کاملSteinitz Theorems for Simple Orthogonal Polyhedra
We define a simple orthogonal polyhedron to be a three-dimensional polyhedron with the topology of a sphere in which three mutually-perpendicular edges meet at each vertex. By analogy to Steinitz’s theorem characterizing the graphs of convex polyhedra, we find graph-theoretic characterizations of three classes of simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric pro...
متن کامل