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If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the ...

The polyhedron compound of the icosahedron (U_(22)) and the great dodecahedron (U_(35)), sometimes known as the small cid. Four faces meet at each edge of the small complex ...

The dual polyhedron of the small dodecicosidodecahedron U_(33) and Wenninger dual W_(72).

The dual polyhedron of the small snub icosicosidodecahedron U_(32) and Wenninger dual W_(110).

The dual polyhedron of the truncated great dodecahedron U_(37) and Wenninger dual W_(75).

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

A roll of two 1s (the lowest roll possible) on a pair of six-sided dice. The probability of rolling snake eyes is 1/36, or 2.777...%.

The geometry of the Lie group R semidirect product with R^2, where R acts on R^2 by (t,(x,y))->(e^tx,e^(-t)y).

A 3-multiperfect number P_3. Six sous-doubles are known (120, 672, 523776, 459818240, 1476304896, and 51001180160; OEIS A005820), and these are believed to comprise all ...