THE CLASSIFICATION AND RELATIONSHIP AMONG THE GEOMETRIC SOLIDS

THE CONCEPT

Cupola series

1. Triangular       cupola                    approach1         approach2     approach3

2. Square            cupola                    approach1        approach2

3. Pentagonal      cupola                   approach1        approach2

4. Triangular Gyrobicupola                  Triangular Orthobicupola

5. Square Gyrobicupola                      Square Orthobicupola

6. Pentagonal Gyrobicupola              Pentagonal Orthobicupola

7. Pentagonal Dipyramid

8. Pentagonal Rotunda

9. Pentagonal Orthobirotunda

10. Pentagonal Orthocupolarotunda      Pentagonal Gyrocupolarotunda

11.   Elongated Square Orthobicupola         Elongated Pentagonal Orthobicupola

The intersection and convex hull of duality

12. The intersection of Tetrahedron dual respect to itself-------------- Octahedron

13. The intersection of cube and Octahedron--------------Cuboctahedron           approach1      approach2

14. The intersection of Dodecuhedron and Icosahedron-----Icosidodecahedron approach1       approach2                        approach3

15. The convex hull of Tetrahedron dual to itself----------------Cube

16. The convex hull of cube dual to Octahedron-----------------Rhombic Dodecahedron

17. The convex hull of Dodecahedron dual to Icosahedron--Rhombic Triacontahedron           approach1                     approach2

Rhombic-series

18. Small Rhombicuboctahedron        approach1        approach2

19. Small Rhombicosidodecahedron

20. Great Rhombicubocatahedron

21. Rhombic  Icosahedron

22. Pentakis    Dodecahedron                  approach1       approach2

23. Deltoidal  Icositetrahedron

Truncated series

24. Truncated  Tetrahedron

25. Truncated  Cube

26. Truncated  Octahedron

27. Truncated  Dodecahedron                    approach1      approah2

28. Truncated  Icosahedron ( Buckyball )              approach1      approah2     approach3

29. Truncated  Icosidodecahedron (  Great  Rhombicosidodecahedron )         approach1      approah2

Triaiks series

30. Triakis  Tetrahedron

31. Triakis  Octahedron

32. Triakis  Icosahedron

33. Tetrakis  Hexahedron

Interesting series

34. 10 Hexagons

35. Great Dodecadodeca

36. Great Dodecahemicosahedron

37. Great Stellated-Dodecahedron

38. Small Stellated-Dodecahedron

39. Five Octahedron in dodecahedron

40. Pentagrammic Antiprism

Prism series

41. Augmented Pentagonal Prism

42. Augmented Hexagonal  Prism

43. Biaugmented Pentagonal Prism

44. Metabiaugmented Hexagonal Prism

45. Parabiaugmented Hexagonal Prism

46. Triaugmented Hexagonal Prism

47. Augmented Dodecahedron

48. Parabiaugmented Dodecahedron

49. Tridiminished Icosahedron

50. Metabidiminished Icosahedron

51. Triangular Hebesphenorotunda

Other

52. Octahedron inscribed a cube

The Relationship