Semi-regular polyhedra

For the infinite semi-regular polyhedra the vertex sums are greater than 360°, depending on the genus g, the total excess being 4ji(gr—1). If the polyhedron is stellated the genus may be fractional, but we are not concerned with this case. 

The polyhedron corresponding to the Neovius surface has the same arrangement of points as that for the infinite semi-regular polyhedral surface 6.43 discussed above, but the spaces between the points are differently filled with polygons so that each of the 48 points per cubic cell has the configuration of 8.4.8.6 and this leads to a surface of genus of 9. This surface has two kinds of flat points and is thus not regular (Mackay Terrones 1991). 12 tubes in the [110] directions connect cavities. 

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