By Bloch S. (ed.)
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Additional resources for Algebraic Geometry - Bowdoin 1985, Part 2
Second order fundamental edge nets and fundamental vertex nets are modifications of first order fundamental edge nets and the same net symbols can be used. L. V. 1 A regular star pentagon (Les Pook, Flexagons inside out, 2003, © Cambridge University Press 2003, reprinted with permission) The fundamental silver edge net and the fundamental bronze edge net are also modifications, but with different net symbols. 11. Heavy lines show that adjacent polygons are not connected. Hinge angles in a net are all the same, but alternate hinge angles are of opposite sign, and most of the nets have a zigzag appearance.
Some of the irregular polygons which have been used in published nets for edge flexagons are given by Conrad and Hartline (1962); McIntosh (2000a, b, c, d), Mitchell (1999) and Pook (2003). Even edge rings of silver triangles and bronze triangles are illustrated in the next section. Further illustrations of edge rings of irregular polygons are included in Chapter 10. 1), and are as follows. 3). 9) between each pair of adjacent polygons. Regular even edge rings of identical irregular convex polygons are always possible.
In a ring symbol for a compound edge ring the number outside the brackets is the number of polygons in the ring and the angles inside the brackets are the hinge angles of alternate polygons. 2). There are no compound edge rings of triangles. There is one possible flat compound edge ring of squares and one of regular pentagons. There are four possible flat compound edge rings of regular hexagons, two of these are included in the table. 5 Flat compound edge rings of regular polygons Polygon type Number in ring Ring symbol Square Pentagon Hexagon Hexagon Octagon Octagon Enneagon Decagon Decagon Decagon Decagon Dodecagon Dodecagon Dodecagon Dodecagon Dodecagon Dodecagon Overlapping ring.
Algebraic Geometry - Bowdoin 1985, Part 2 by Bloch S. (ed.)