Below are the 60 matrices used to generate a complete
icosahedral particle given the transformed coordinates
for each entry in the index of virus structures. The matrix numbers below (1-60) place the asymmetric unit in the capsid as shown in the figures above. The numbering of asymmetric units for other T-number cages is the same as that of the T=1 cage.
| 1) | |
|
| | 1.00000 | 0.00000 | 0.00000 | | 0.00000 | 1.00000 | 0.00000 | | 0.00000 | 0.00000 | 1.00000 |
|
| 2) | |
|
| | 0.30902 | -0.80902 | 0.50000 | | 0.80902 | 0.50000 | 0.30902 | | -0.50000 | 0.30902 | 0.80902 |
|
| 3) | |
|
| | -0.80902 | -0.50000 | 0.30902 | | 0.50000 | -0.30902 | 0.80902 | | -0.30902 | 0.80902 | 0.50000 |
|
| 4) | |
|
| | -0.80902 | 0.50000 | -0.30902 | | -0.50000 | -0.30902 | 0.80902 | | 0.30902 | 0.80902 | 0.50000 |
|
| 5) | |
|
| | 0.30902 | 0.80902 | -0.50000 | | -0.80902 | 0.50000 | 0.30902 | | 0.50000 | 0.30902 | 0.80902 |
|
| 6) | |
|
| | -1.00000 | 0.00000 | 0.00000 | | 0.00000 | -1.00000 | 0.00000 | | 0.00000 | 0.00000 | 1.00000 |
|
| 7) | |
|
| | -0.30902 | -0.80902 | 0.50000 | | 0.80902 | -0.50000 | -0.30902 | | 0.50000 | 0.30902 | 0.80902 |
|
| 8) | |
|
| | 0.30902 | 0.80902 | 0.50000 | | -0.80902 | 0.50000 | -0.30902 | | -0.50000 | -0.30902 | 0.80902 |
|
| 9) | |
|
| | -0.30902 | 0.80902 | 0.50000 | | -0.80902 | -0.50000 | 0.30902 | | 0.50000 | -0.30902 | 0.80902 |
|
| 10) | |
|
| | -0.50000 | 0.30902 | 0.80902 | | 0.30902 | -0.80902 | 0.50000 | | 0.80902 | 0.50000 | 0.30902 |
|
| 11) | |
|
| | 0.50000 | -0.30902 | 0.80902 | | -0.30902 | 0.80902 | 0.50000 | | -0.80902 | -0.50000 | 0.30902 |
|
| 12) | |
|
| | 0.80902 | 0.50000 | 0.30902 | | -0.50000 | 0.30902 | 0.80902 | | 0.30902 | -0.80902 | 0.50000 |
|
| 13) | |
|
| | 0.80902 | -0.50000 | -0.30902 | | 0.50000 | 0.30902 | 0.80902 | | -0.30902 | -0.80902 | 0.50000 |
|
| 14) | |
|
| | 0.50000 | 0.30902 | -0.80902 | | 0.30902 | 0.80902 | 0.50000 | | 0.80902 | -0.50000 | 0.30902 |
|
| 15) | |
|
| | -0.50000 | -0.30902 | -0.80902 | | -0.30902 | -0.80902 | 0.50000 | | -0.80902 | 0.50000 | 0.30902 |
|
| 16) | |
|
| | -0.30902 | -0.80902 | -0.50000 | | 0.80902 | -0.50000 | 0.30902 | | -0.50000 | -0.30902 | 0.80902 |
|
| 17) | |
|
| | 0.30902 | -0.80902 | -0.50000 | | 0.80902 | 0.50000 | -0.30902 | | 0.50000 | -0.30902 | 0.80902 |
|
| 18) | |
|
| | -0.30902 | 0.80902 | -0.50000 | | -0.80902 | -0.50000 | -0.30902 | | -0.50000 | 0.30902 | 0.80902 |
|
| 19) | |
|
| | 0.50000 | -0.30902 | -0.80902 | | -0.30902 | 0.80902 | -0.50000 | | 0.80902 | 0.50000 | 0.30902 |
|
| 20) | |
|
| | -0.50000 | 0.30902 | -0.80902 | | 0.30902 | -0.80902 | -0.50000 | | -0.80902 | -0.50000 | 0.30902 |
|
| 21) | |
|
| | -0.80902 | -0.50000 | -0.30902 | | 0.50000 | -0.30902 | -0.80902 | | 0.30902 | -0.80902 | 0.50000 |
|
| 22) | |
|
| | 0.80902 | 0.50000 | -0.30902 | | -0.50000 | 0.30902 | -0.80902 | | -0.30902 | 0.80902 | 0.50000 |
|
| 23) | |
|
| | 0.80902 | -0.50000 | 0.30902 | | 0.50000 | 0.30902 | -0.80902 | | 0.30902 | 0.80902 | 0.50000 |
|
| 24) | |
|
| | -0.80902 | 0.50000 | 0.30902 | | -0.50000 | -0.30902 | -0.80902 | | -0.30902 | -0.80902 | 0.50000 |
|
| 25) | |
|
| | -0.50000 | -0.30902 | 0.80902 | | -0.30902 | -0.80902 | -0.50000 | | 0.80902 | -0.50000 | 0.30902 |
|
| 26) | |
|
| | 0.50000 | 0.30902 | 0.80902 | | 0.30902 | 0.80902 | -0.50000 | | -0.80902 | 0.50000 | 0.30902 |
|
| 27) | |
|
| | 0.00000 | 0.00000 | 1.00000 | | 1.00000 | 0.00000 | 0.00000 | | 0.00000 | 1.00000 | 0.00000 |
|
| 28) | |
|
| | 0.00000 | 1.00000 | 0.00000 | | 0.00000 | 0.00000 | 1.00000 | | 1.00000 | 0.00000 | 0.00000 |
|
| 29) | |
|
| | 0.00000 | -1.00000 | 0.00000 | | 0.00000 | 0.00000 | 1.00000 | | -1.00000 | 0.00000 | 0.00000 |
|
| 30) | |
|
| | 0.00000 | 0.00000 | -1.00000 | | -1.00000 | 0.00000 | 0.00000 | | 0.00000 | 1.00000 | 0.00000 |
|
| 31) | |
|
| | 0.00000 | -1.00000 | 0.00000 | | 0.00000 | 0.00000 | -1.00000 | | 1.00000 | 0.00000 | 0.00000 |
|
| 32) | |
|
| | 0.00000 | 1.00000 | 0.00000 | | 0.00000 | 0.00000 | -1.00000 | | -1.00000 | 0.00000 | 0.00000 |
|
| 33) | |
|
| | -0.80902 | -0.50000 | 0.30902 | | -0.50000 | 0.30902 | -0.80902 | | 0.30902 | -0.80902 | -0.50000 |
|
| 34) | |
|
| | 0.80902 | -0.50000 | -0.30902 | | -0.50000 | -0.30902 | -0.80902 | | 0.30902 | 0.80902 | -0.50000 |
|
| 35) | |
|
| | 0.50000 | 0.30902 | -0.80902 | | -0.30902 | -0.80902 | -0.50000 | | -0.80902 | 0.50000 | -0.30902 |
|
| 36) | |
|
| | -0.30902 | -0.80902 | -0.50000 | | -0.80902 | 0.50000 | -0.30902 | | 0.50000 | 0.30902 | -0.80902 |
|
| 37) | |
|
| | -0.80902 | 0.50000 | -0.30902 | | 0.50000 | 0.30902 | -0.80902 | | -0.30902 | -0.80902 | -0.50000 |
|
| 38) | |
|
| | -0.50000 | -0.30902 | -0.80902 | | 0.30902 | 0.80902 | -0.50000 | | 0.80902 | -0.50000 | -0.30902 |
|
| 39) | |
|
| | -0.50000 | 0.30902 | -0.80902 | | -0.30902 | 0.80902 | 0.50000 | | 0.80902 | 0.50000 | -0.30902 |
|
| 40) | |
|
| | 0.00000 | 0.00000 | -1.00000 | | 1.00000 | 0.00000 | 0.00000 | | 0.00000 | -1.00000 | 0.00000 |
|
| 41) | |
|
| | -0.80902 | 0.50000 | 0.30902 | | 0.50000 | 0.30902 | 0.80902 | | 0.30902 | 0.80902 | -0.50000 |
|
| 42) | |
|
| | 0.80902 | 0.50000 | -0.30902 | | 0.50000 | -0.30902 | 0.80902 | | 0.30902 | -0.80902 | -0.50000 |
|
| 43) | |
|
| | -0.30902 | 0.80902 | -0.50000 | | 0.80902 | 0.50000 | 0.30902 | | 0.50000 | -0.30902 | -0.80902 |
|
| 44) | |
|
| | 0.50000 | -0.30902 | -0.80902 | | 0.30902 | -0.80902 | 0.50000 | | -0.80902 | -0.50000 | -0.30902 |
|
| 45) | |
|
| | -0.80902 | -0.50000 | -0.30902 | | -0.50000 | 0.30902 | 0.80902 | | -0.30902 | 0.80902 | -0.50000 |
|
| 46) | |
|
| | -0.30902 | -0.80902 | 0.50000 | | -0.80902 | 0.50000 | 0.30902 | | -0.50000 | -0.30902 | -0.80902 |
|
| 47) | |
|
| | -0.30902 | 0.80902 | 0.50000 | | 0.80902 | 0.50000 | -0.30902 | | -0.50000 | 0.30902 | -0.80902 |
|
| 48) | |
|
| | 1.00000 | 0.00000 | 0.00000 | | 0.00000 | -1.00000 | 0.00000 | | 0.00000 | 0.00000 | -1.00000 |
|
| 49) | |
|
| | 0.30902 | 0.80902 | -0.50000 | | 0.80902 | -0.50000 | -0.30902 | | -0.50000 | -0.30902 | -0.80902 |
|
| 50) | |
|
| | 0.30902 | -0.80902 | -0.50000 | | -0.80902 | -0.50000 | 0.30902 | | -0.50000 | 0.30902 | -0.80902 |
|
| 51) | |
|
| | -1.00000 | 0.00000 | 0.00000 | | 0.00000 | 1.00000 | 0.00000 | | 0.00000 | 0.00000 | -1.00000 |
|
| 52) | |
|
| | 0.80902 | 0.50000 | 0.30902 | | 0.50000 | -0.30902 | -0.80902 | | -0.30902 | 0.80902 | -0.50000 |
|
| 53) | |
|
| | 0.30902 | -0.80902 | 0.50000 | | -0.80902 | -0.50000 | -0.30902 | | 0.50000 | -0.30902 | -0.80902 |
|
| 54) | |
|
| | -0.50000 | 0.30902 | 0.80902 | | -0.30902 | 0.80902 | -0.50000 | | -0.80902 | -0.50000 | -0.30902 |
|
| 55) | |
|
| | 0.00000 | 0.00000 | 1.00000 | | -1.00000 | 0.00000 | 0.00000 | | 0.00000 | -1.00000 | 0.00000 |
|
| 56) | |
|
| | 0.50000 | -0.30902 | 0.80902 | | 0.30902 | -0.80902 | -0.50000 | | 0.80902 | 0.50000 | -0.30902 |
|
| 57) | |
|
| | 0.30902 | 0.80902 | 0.50000 | | 0.80902 | -0.50000 | 0.30902 | | 0.50000 | 0.30902 | -0.80902 |
|
| 58) | |
|
| | 0.80902 | -0.50000 | 0.30902 | | -0.50000 | -0.30902 | 0.80902 | | -0.30902 | -0.80902 | -0.50000 |
|
| 59) | |
|
| | -0.50000 | -0.30902 | 0.80902 | | 0.30902 | 0.80902 | 0.50000 | | -0.80902 | 0.50000 | -0.30902 |
|
| 60) | |
|
| | 0.50000 | 0.30902 | 0.80902 | | -0.30902 | -0.80902 | 0.50000 | | 0.80902 | -0.50000 | -0.30902 |
|
