Amphicheiral knots with n = 12 crossings are derived by M.Hasseman [47]. After the correction for the knot 10. 26 and identification of 7 duplications [48], their complete list that consists of 54 knots, given by Conway symbols showing their (anti)symmetry, is the following:
 01. 62 02. 5125 03. (3,3)2 04. 321123 05. 34 06. (21,21)2 07. 312213 08. 221422 09. 2182 10. 26 11. 4224 12. 21212212 13. (211,2)2 14. (3,2+)2 15. (21,2+)2 16 = 13 17. (22,2)2 18. 2422 19. 2.2.2.2.20.20 20. 20.21.21.20 21. 2.2.20.2.2.20 22. 12L 23. 10**:20::.20 24. 10*20:::20 25. 8*.20:2.2:20 26. 8*2.2.2.2 27. 2.21.21.2 28. .21.21.2.2 29. 3.2.2.3 30. .3.3.2.2 31. 12K 32. 8*2.20.20.2 33. 8*.21.21 34. 8*2.2:.20.20 35. 10**20::.20 36 = 20 37. 8*210:.210 38. .4.4 39. .31.31 40. 8*20.20:.20.20 41. 8*3.3 42. 8*30.30 43. 10*2::.2 44. 10**:2::.2 45. 10**2::.2 46. 8*20.20.20.20 47. 30.2.2.30 48. 8*3:.3 49. 8*30:.30 50. .22.22 51 = 50 52. .3.3.20.20 53. 10**2::::2 54 = 40 55. 10**:20.20 56. 10**:2.2 57 = 45 58. 12B 59. .21.2.210.20 60 = 59 61 = 6

 Amphicheiral knot H59=H60 and two of its vertex-antisymmetrical 3D-presentations, based on the antiinversion.

 Even in the case when the polynomial d(t) and Liang polynomial are not able to recognize some concealed antisymmetry, it could be seen from the corresponding vertex-bicolored diagrams. For example, in the case of the 14-crossing amphicheiral knot for which the both polynomials failed, its amphicheirality could be explained by the presence of rotational antireflection, i.e. by geometrical antisymmetry arguments. Antisymmetrical knot diagrams, rigid and non-rigid achirality are considered by J.Liang & K.Mislow [22] and E.Flapan [29].