1. Between 1985 and 1990 more than half a dozen publications claimed we were wrong

2. 1

3. image at: commons.wikimedia.org/wiki/File:Endohedral_fu... commons.wikimedia.org/wiki/File:Endohedral_fu...

4. 2

5. One can tile a flat floor with squares

7. And one can tile a flat floor with hexagons

8. But one cannot tile a flat floor with pentagons

9. David Jones pseudonym of Daedalus in the New Scientist (1966)

10. A sheet of hexagons no matter how large can only close if there are exactly 12 pentagons interspersed

11. But with pentagons…..

12. There is also a problem when you try to tile a flat surface with hexagons around a pentagon

13. But if we allow curvature

14. And add some more pentagons

15. We find that with 12 pentagons the network closes into a cage

16. © The Pentagon Isolation Rule (PIR) Now if 12 pentagons are needed to close a cage 60 carbon atoms are needed if adjacent pentagons areto be avoided we know adjacent pentagons are bad news from our Organic Chemistry

17. © Then we realised it was the same pattern as football So how could it be wrong?

18. 3

19. Then while building models like this little boy

20. I guessed that C 62, C 64, C 66 and C 68 cannot close unless some pentagons are adjacent but we knew that C 70 CAN! This was proven mathematically by Schmalz et al in Galveston

22. C 70 The cage solution explained why 60 and 70 were both special

23. 4

24. Then again while playing around with models like this little boy

25. C 28 should be special - a tetravalent “Superatom” atom H W Kroto, Nature, 329, 529 (1987) Polaroid image of the first molecular model of C 28

26. Mass spectrum of laser vapourised graphite (Rice 1985) C 28

27. Ti @ C 28 Ti

28. U@C 28 Paul Dunk and Alan Marshall U

29. 5

31. The first giant fullerene C 240 with Ken McKay Nature 1988

32. C 540 made by Ken McKay

36. C 60 C 240 C 540 C 960 The Giant Fullerenes with Ken McKay Nature 331, 328 (1988) Sussex NNC

40. http://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/jsmn.htm

41. C 28 Sussex NNC

42. Exxon Data Cox et al JACS 110 1588 (1988) Sussex NNC Assignment

43. ©

44. The Pentagon Isolation Rule (PIR)

45. Sussex NNC Rice

46. Sussex NNC

47. After C 60 the next fullerene which can have non abutting pentagons is C 70

48. If C 60 is a cage

49. then C 70 MUST be the next magic number

50. If C 60 is a cage then C 70 MUST be the next magic number Pentagon Isolation Rule prediction Kroto 1986 and Schmalz et al 1986

51. © So… C 60 is the smallest cage that can avoid abutting pentagons

53. But if we do not constrain to a flat surface and allow the network to curveC

56. David Jones in a fun article published under the pseudonym of Daedalus in the New Scientist (1966) pointed out that a sheet of hexagons no matter how large could only close if there were exactly 12 pentagons interspersed

57. © The Pentagon Isolation Rule (PIR) C 60 is the smallest fullerene that can avoid abutting pentagons

58. Sussex NNC C 24

59. Sussex NNC C 20

60. Sussex NNC It is not possible to make a C 22 cage

61. NB – Paquette’s Group had synthesised Dodecahedrane C 20 H 20 in 1982, three years before the discovery of C 60

62. With hindsight C 20 H 20 can be recognised as the fully hydrogenated derivative of C 20 the smallest possible and almost certainly least stable fullerene

63. With hindsight C 20 H 20 can be recognised as the fully hydrogenated derivative of C 20 the smallest possible and least stable fullerene

64. C 50 Cl 10 was isolated in 2004

66. C 11 + 4n+2 rule (4n+3)-1 rule yields 11, 15, 19, 23 C 15 + C 19 + C 23 +

67. C 28 ”superatom” analogue of sp 3 carbon atom Suggests T d C 28 H 4 Nature 329 529 (1987) Support U @ C 28 U tetravalent (Smalley and coworkers) C 28 H 4 Sussex NNC

68. Kroto and Walton Chem Phys Letts 1993 C 24 H 12

69. C 32 H 2

70. C 36 H 12

71. C 50 H 10 predicted to be stable 1993

72. Sussex NNC The Oddfellas ?

73. C 20 ? Sussex NNC

74. C 20 ? Sussex NNC

75. The Multiplet Pentagon Isolation Rule

76. Sussex NNC

78. NB – Paquette’s Group had synthesised Dodecahedrane C 20 H 20 in 1982, three years before the discovery of C 60 With hindsight C 20 H 20 can be recognised as the fully hydrogenated derivative of C 20 the smallest possible and least stable fullerene

79. NB – Paquette’s Group had synthesised Dodecahedrane C 20 H 20 in 1982, three years before the discovery of C 60 With hindsight C 20 H 20 can be recognised as the fully hydrogenated derivative of C 20 the smallest possible and least stable fullerene

80. Sussex NNC

81. Moses Gomberg’s Free Radical (1901) triphenyl methyl CPh 3 -CPh 3 ⇄. CPh 3 +. CPh 3

82. C 28 H 4

83. C 50 H 10

86. Sussex NNC Rice

87. Sussex NNC

88. C 28 H 4

89. Exxon Data Cox et al JACS 110 1588 (1988) Sussex NNC Assignment

90. BuckyWorld ©

91. Sussex NNC