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One of the eight convex deltahedra built up from 16 equilateral triangles. It consists of two oppositely faced square pyramids rotated 45 degrees to each other and separated ...

A Heegaard splitting of a connected orientable 3-manifold M is any way of expressing M as the union of two (3,1)-handlebodies along their boundaries. The boundary of such a ...

The Heronian mean of two numbers a and b is defined as HM(a,b) = 1/3(2A+G) (1) = 1/3(a+sqrt(ab)+b), (2) where A is the arithmetic mean and G the geometric mean. It arises in ...

A pyramid with a hexagonal base. The edge length of a hexagonal pyramid of height h is a special case of the formula for a regular n-gonal pyramid with n=6, given by ...

A hexagrammic prism is a prism formed by two regular hexagrams offset along their symmetry axis and with corresponding edges connected by lateral faces. For an equilateral ...

The following three pieces of information completely determine the homeomorphic type of a surface (Massey 1996): 1. Orientability, 2. Number of boundary components, 3. Euler ...

A point p on a regular surface M in R^3 is said to be hyperbolic if the Gaussian curvature K(p)<0 or equivalently, the principal curvatures kappa_1 and kappa_2, have opposite ...

A 4-hyperboloid has negative curvature, with R^2=x^2+y^2+z^2-w^2 (1) 2x(dx)/(dw)+2y(dy)/(dw)+2z(dz)/(dw)-2w=0. (2) Since r=xx^^+yy^^+zz^^, (3) it follows that ...

The polyhedron compound of the icosidodecahedron and its dual, the rhombic triacontahedron. The compound can be constructed from an icosidodecahedron of unit edge length by ...

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...