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The four planes determined by the four altitudes of a tetrahedron and the orthocenters of the corresponding faces pass through the Monge point of the tetrahedron.

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

A broad area of mathematics connected with functional analysis, differential equations, index theory, representation theory, and mathematical physics.

The set of all points x that can be put into one-to-one correspondence with sets of essentially distinct values of five homogeneous coordinates x_0:x_1:x_2:x_3:x_4, not all ...

A nonsimply connected 3-manifold, also called a dodecahedral space.

If del xF=0 (i.e., F(x) is an irrotational field) in a simply connected neighborhood U(x) of a point x, then in this neighborhood, F is the gradient of a scalar field phi(x), ...

A polygrammic prism is a prism formed by two regular polygrams offset along their symmetry axis and with corresponding edges connected by lateral faces. The hexagrammic prism ...

A phase curve (i.e., an invariant manifold) which meets a hyperbolic fixed point (i.e., an intersection of a stable and an unstable invariant manifold) or connects the ...

The set of all points x that can be put into one-to-one correspondence with sets of essentially distinct values of four homogeneous coordinates x_0:x_1:x_2:x_3, not all ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...