Flexagon Index

Cambridge University Press 0521819709 - Flexagons Inside Out Les Pook Index More information

Flexagon index

compound hexagon flexagon, 4-cycle pentagon flexagon 136 regular 5, 5 99–102 compound pentagon flexagon, 3-cycle regular 5, 5/2 102 131–2 two incomplete principal cycles compound rhombus flexagon, 3-cycle principal main position link 144–5 102 compound square flexagon subsidiary main position links 3-cycle 127–8 102–6 5-cycle 128 rectangle flexagon, four faced 140 digon flexagon 87 rhombus flexagon, four faced truncated 87–8 three sectors 140–2 double hinged 88–9 two sectors 143–4 distorted hexagon flexagon, six faced right angle triangle flexagon 146–9 four faced 153 three faced 151–3 hexaflexagon ring pentagon flexagon, regular single five faced 41 principal cycle 123 four faced 36–8, 52 hexa(hexaflexagon) 15, 39–40, square flexagon 49–51 five faced 76–8 puzzle 44–6 incomplete cycle 55–8, 64–5 null 32–3 irregular cycle 24–8, 54 seven faced 42 truncated 95 tri(hexaflexagon) 5–7, 14, 15, 30, irregular cycle and incomplete 33–6 cycle, main position link decorated 35–6 66 hexagon flexagon, single principal main position link and box position cycle links 74–6 irregular 109–10 puzzle 74–6, 81 regular 108 regular cycle and incomplete cycle, hybrid flexagon 89 main position link 65–6 regular cycle 54–5, 58–9 octagon flexagon truncated 93–5 regular 8, 8 113–15 regular cycle and irregular cycle, three faced 115–18 main position link 63–4

167

168 Flexagon index

square flexagon (cont.) two irregular cycles, box position simple 7 links 72–4 two incomplete cycles, box position two regular cycles, main position links 71–2 link 60–1, 79–81 two incomplete cycles, main star octagon flexagon 120–1 position link 66, 79–81 two irregular cycles, main position triangle flexagon, single cycle 48–9 link 63 truncated 91

Subject index

assembly instructions 8–13 flexagon incomplete 54, 56–8 box flex 70–1 irregular 28, 54 box position 27, 85 regular 30, 54, 55 links 71, 72 Flexagon Committee 15, 16 flexagon diagram 29 compound flexagons 123–36, 144–5 flexagon figure 29, 30, 58–9, 99 compound hexagon flexagons 132–6 modified 125–26 compound pentagon flexagons flexagon symbol 30 128–32 flexahedra 154–63 compound rhombus flexagon 144–5 flexatube 89–90 compound square flexagons 126–8 full map 24–7 convex polygon flexagons 82–118 cube flexahedra 158–63 geometry of flexagons 18–30 cycle 7, 19 complete 54 hexaflexagons 31–52 incomplete 54 hexagon flexagons 85, 106–10, 132–6, irregular 63 146–9 principal 20–1, 83 hinged 19, 155 regular 60–1 history of flexagons 14–17 subsidiary 20–1, 83 Hooke’s universal joint 88 hyperflat 155 degrees of freedom 21, 23 hexaflexagons 32–3 interleaf flex 78–81 hexagon flexagons 85 intermediate position 6 octagon flexagons 86–7 codes 26–7, 27, 58–60 pentagon flexagons 85 map 29, 91, 140 Sarrut’s parallel motion 23 square flexagons 24, 58, 85 leaves 6 triangle flexagons 49, 85 linkages 21 design of flexagons 40–2, 64–5, 71, 148–9 main position 5 digon flexagons 87–9 codes 24–5 distorted polygon flexagons 137–53 flat 20 link 36, 59–60 face arrangements 42–6, 76–8 principal 20, 97–8

169

170 Subject index

main position (cont.) right angle triangle flexagons skew 20 149–53 slant 20 ring flexagons 119–36 subsidiary 20, 97–8 link 101–2, 106 Sarrut’s parallel motion 22–3 Mobius¨ band 33 Schlafli¨ symbol 30 sector 25 octagon flexagons 86–7, 110–18 simplified map 28, 117 origami with hexaflexagons 52 snap flex 98 square flexagons 53–81, 85, 93–5, pat 6, 27–8 126–8 pentagon flexagons 98–106, 128–32 star flexagons 120–1 pinch flex 6–7, 158 polygon rings, 121–2, 123–4, 126–7, triangle flexagons 47–9 85, 131, 132–3 90–1 prism flexahedra 155–7 Tuckerman diagram 28–9, 128, pseudocycle 72 153 push through flex 88 Tuckerman traverse 38–9, 62, pyramid flexahedra 157–8 65–6 twist flex 113, 117, 118 rectangle flexagon 140 rhombus flexagons 140–5 V-flex 49–51