Archimedean duals

==Catalan polyhedra]]
The Catalan polyhedra are the dual of the convex Archimedean polyhedra. There are 13 Catalan polyhedra.

### Duals of truncated Platonic polyhedra

C1. Triakis tetrahedron (dual of Truncated tetrahedron)

C2. Triakis octahedron (dual of Truncated cube)

C3. Tetrakis hexahedron (dual of Truncated octahedron)

C4. Triakis icosahedron (dual of Truncated dodecahedron)

C5. Pentakis dodecahedron (dual of Truncated icosahedron)

### Duals of quasiregular convex polyhedra

C6. Rhombic dodecahedron (dual of Cuboctahedron)

C7. Rhombic triacontahedron (dual of Icosidodecahedron)

### Duals of convex trapeziverts

C8. Deltoidal icositetrahedron (dual of Small rhombicuboctahedron)

C9. Deltoidal hexecontahedron (dual of Small rhombicosidodecahedron)

### Duals of convex omnitruncated polyhedra

C9. Disdyakis dodecahedron (dual of Great rhombicuboctahedron)

C10. Disdyakis triacontahedron (dual of Great rhombicosidodecahedron)

### Duals of convex snub polyhedra

C11. Pentagonal icositetrahedron (dual of Snub cube)

C12. Pentagonal hexecontahedron (dual of Snub dodecahedron)

## Duals of non-convex Archimedean polyhedra

### Duals of truncates of the Kepler-Poinsot polyhedra

D1. Small stellapentakis dodecahedron (dual of Truncated great dodecahedron)

D2. Great stellapentakis dodecahedron (dual of Truncated great icosahedron)

D3. Great triakis octahedron (dual of Quasitruncated hexahedron)

D4. Great pentakis dodecahedron (dual of Quasitruncated small stellated dodecahedron)

D5. Great triakis icosahedron (dual of Quasitruncated great stellated dodecahedron)

### Duals of non-convex quasiregular polyhedra

D6. Tetrahemihexacron (dual of Tetrahemihexahedron)

D7. Octahemioctacron (dual of Octahemioctahedron)

D8. Hexahemioctacron(dual of Cubohemioctahedron)

D9. Small dodecahemidodecacron (dual of Small dodecahemidodecahedron)

D10. Small icosihemidodecacron (dual of Small icosihemidodecahedron)

D11. Medial rhombic triacontahedron (dual of Dodecadodecahedron)

D12. Small dodecahemicosacron (dual of Small dodecahemicosahedron)

D13. Great dodecahemicosacron (dual of Great dodecahemicosahedron)

D14. Great rhombic triacontahedron (dual of Great icosidodecahedron)

D15. Great dodecahemidodecacron (dual of Great dodecahemidodecahedron)

D16. Great icosihemidodecacron (dual of Great icosihemidodecahedron)

D17. Small triambic icosahedron (dual of Small ditrigonary icosidodecahedron)

D18. Medial triambic icosahedron (dual of Ditrigonary dodecadodecahedron)

D19. Great triambic icosahedron (dual of Great ditrigonary icosidodecahedron)

### Duals of non-convex trapeziverts

D20. Small hexacronic icositetrahedron (dual of Small cubicuboctahedron)

D21. Small rhombihexacron (dual of Small rhombihexahedron)

D22. Small dodecacronic hexecontahedron (dual of Small dodecicosidodecahedron)

D23. Small rhombidodecacron (dual of Small rhombidodecahedron)

D24. Medial deltoidal hexecontahedron (dual of Rhombidodecadodecahedron)

D25. Medial icosacronic hexecontahedron (dual of Icosidodecadodecahedron)

D26. Rhombicosacron (dual of Rhombicosahedron)

D27. Great hexacronic icositetrahedron (dual of Great cubicuboctahedron)

D28. Great deltoidal icositetrahedron (dual of Quasirhombicuboctahedron)

D29. Great rhombihexacron (dual of Great rhombihexahedron)

D30. Great ditrigonal dodecacronic hexecontahedron (dual of Great ditrigonary dodecicosidodecahedron)

D31. Great icosacronic hexecontahedron (dual of Great icosicosidodecahedron)

D32. Great dodecicosacron (dual of Great dodecicosahedron)

D33. Small icosacronic hexecontahedron (dual of Small icosicosidodecahedron)

D34. Small ditrigonal dodecacronic hexecontahedron (dual of Small ditrigonary dodecicosidodecahedron)

D35. Small dodecicosacron (dual of Small dodecicosahedron)

D36. Great dodecacronic hexecontahedron (dual of Great dodecicosidodecahedron)

D37. Great deltoidal hexecontahedron (dual of Quasirhombicosidodecahedron)

D38. Great rhombidodecacron (dual of Great rhombidodecahedron)

### Duals of non-convex omnitruncated polyhedra

D39. Great disdyakis dodecahedron (dual of Quasitruncated cuboctahedron)

D40. Medial disdyakis triacontahedron (dual of Quasitruncated dodecadodecahedron)

D41. Great disdyakis triacontahedron (dual of Great quasitruncated icosidodecahedron)

D42. Tetradyakis hexahedron (dual of Cuboctatruncated cuboctahedron)

D43. Tridyakis icosahedron (dual of Icosidodecatruncated icosidodecahedron]])

### Duals of non-convex snub polyhedra

D44. Medial pentagonal hexecontahedron (dual of Snub dodecadodecahedron)

D45. Great pentagonal hexecontahedron (dual of Great snub icosidodecahedron)

D46. Small hexagonal hexecontahedron (dual of Small snub icosicosidodecahedron)

D47. Medial inverted pentagonal hexecontahedron (dual of Inverted snub dodecadodecahedron)

D48. Great inverted pentagonal hexecontahedron (dual of Great inverted snub icosidodecahedron)

D49. Medial hexagonal hexecontahedron (dual of Snub icosidodecadodecahedron)

D50. Great hexagonal hexecontahedron (dual of Great snub dodecicosidodecahedron)

D51. Great pentagrammic hexecontahedron (dual of Great inverted retrosnub icosidodecahedron)

D52. Small hexagrammic hexecontahedron (dual of Small inverted retrosnub icosicosidodecahedron)

D53. Great dirhombicosidodecacron (dual of Great dirhombicosidodecahedron)

## Footnotes

1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 As these polyhedra have faces that pass through the centre, the duals are all infinite in extent.