Symmetry Groups
The vast majority of all the muqarnas forms I have developed are based upon the 32-fold symmetry shown at the left. An animation of it can be viewed here. This symmetry group possesses sixteen (16) unique tile/surface types. They can be seen here.
Below the comments section is a table with information about symmetry groups suitable for mogharnas including and beyond those already being investigated.
Below the comments section is a table with information about symmetry groups suitable for mogharnas including and beyond those already being investigated.
Plan View of 36-Fold Symmetry Central Mogharnas Dome
Creates a set of 18 unique muqarnas tiles
Plan View of 32-Fold Symmetry Central Mogharnas Dome
Creates a set of 16 unique muqarnas tiles
Plan View of 14-Fold Symmetry Central Mogharnas Dome
Creates a set of 7 unique muqarnas tiles
Plan View of 10-Fold Symmetry Central Mogharnas Dome
Creates a set of 5 unique muqarnas tiles
Plan View of 8-Fold Symmetry Central Mogharnas Dome
Creates a set of 4 unique muqarnas tiles
Mogharnas / Muqarnas
Click What You Want To See
Symmetry Group Properties
1.) Symmetry groups for which I’ve designed tile/surface sets and developed muqarnas are underlined in bold.
2.) Sometimes 1.) also includes complete surface/tile sets for other ‘contained’ symmetry groups that are underlined only. For example the animation on the Cruciform page shows the regular dome for the 32-fold tile/surface set and shows the regular domes which can be made from that set. This includes the 16-fold, 8-fold, and 4-fold regular domes. None of these domes include the vertical tile/surface, but they could have.
2.) Sometimes 1.) also includes complete surface/tile sets for other ‘contained’ symmetry groups that are underlined only. For example the animation on the Cruciform page shows the regular dome for the 32-fold tile/surface set and shows the regular domes which can be made from that set. This includes the 16-fold, 8-fold, and 4-fold regular domes. None of these domes include the vertical tile/surface, but they could have.
| N, integer | (360/N)° | Number of Surfaces | All ∠° | Prime Factors | Symmetry Groups |
|---|---|---|---|---|---|
| 2 | 180° | 1 | 180° | 2 | 2 |
| 3 | 120° | 1 | 120° | 3 | 3 |
| 4 | 90° | 2 | 90° 180° | 2, 2 | 2, 4 |
| 5 | 72° | 2 | 72° 144° | 5 | 5 |
| 6 | 60° | 3 | 60° 120° 180° | 2, 3 | 2, 3, 6 |
| 7 | 51.4° | 3 | 51.4° 102.9° 154.3° | 7 | 7 |
| 8 | 45° | 4 | 45° 90° 135° 180° | 2, 2, 2 | 2, 4, 8 |
| 9 | 40° | 4 | 40° 80° 120° 160° | 3, 3 | 3, 9 |
| 10 | 36° | 5 | 36° 72° 108° 144° 180° | 2, 5 | 2, 5, 10 |
| 11 | 32.7° | 5 | 32.7° 65.5° 98.2° 130.9° 163.6° | 11 | 11 |
| 12 | 30° | 6 | 30° 60° 90° 120° 150° 180° | 2, 2, 3 | 2, 3, 4, 6, 12 |
| 13 | 27.7° | 6 | 27.7° 55.4° 83.1° 110.8° 138.7° 166.2° | 13 | 13 |
| 14 | 25.7° | 7 | 25.7°, 51.4°, 77.1°, 102.9°, 128.6°, 154.3°, 180° | 2, 7 | 2, 7, 14 |
| 15 | 24° | 7 | 24° 48° 72° 96° 120° 144° 168° | 3, 5 | 3, 5, 15 |
| 16 | 22.5° | 8 | 22.5° 45° 67.5° 90° 112.5° 135° 157.5° 180° | 2, 2, 2, 2 | 2, 4, 8, 16 |
| 17 | 21.2° | 8 | 21.2° 42.4° 63.5° 84.7° 105.9° 127.1° 148.2° 169.4° | 17 | 17 |
| 18 | 20° | 9 | 20° 40° 60° 80° 100° 120° 140° 160° 180° | 2, 3, 3 | 2, 3, 6, 9, 18 |
| 19 | 18.9° | 9 | 18.9° 37.9° 56.8° 75.8° 94.7° 113.7° 132.6° 151.6° 170.5° | 19 | 19 |
| 20 | 18° | 10 | 18° 36° 54° 72° 90° 108° 126° 144° 162° 180° | 2, 2, 5 | 2, 4, 5, 10, 20 |
| 21 | 17.1° | 10 | 17.1° 34.3° 51.4° 68.6° 85.7° 102.9° 120° 137.1° 154.3° 171.4° | 3, 7 | 3, 7, 21 |
| 22 | 16.4° | 11 | 16.4° 32.7° 49.1° 65.5° 81.8° 98.2° 114.5° 130.9° 147.3° 163.6° 180° | 2, 11 | 2, 11, 22 |
| 23 | 15.7° | 11 | 15.7° 31.3° 47.0° 62.6° 78.3° 93.9° 109.6° 125.2° 140.9° 156.5° 172.2° | 23 | 23 |
| 24 | 15° | 12 | 15° 30° 45° 60° 75° 90° 105° 120° 135° 150° 165° 180° | 2, 2, 2, 3 | 2, 3, 4, 6, 8, 12, 24 |
| 25 | 14.4° | 12 | 14.4° 28.8° 43.2° 57.6° 72° 86.4° 100.8° 115.2° 129.6° 144° 158.4° 172.8° | 5, 5 | 5, 25 |
| 26 | 13.8° | 13 | 13.8° 27.7° 41.5° 55.4° 69.2° 83.1° 96.9° 110.8° 124.6° 138.5° 152.3° 166.2° 180° | 2, 13 | 2, 13, 26 |
| 27 | 13.3° | 13 | 13.3° 26.7° 40° 53.3° 66.7° 80° 93.3° 106.7° 120° 133.3° 146.7° 160° 173.3° | 3, 3, 3 | 3, 9, 27 |
| 28 | 12.9° | 14 | 12.9° 25.7° 38.6° 51.4° 64.3° 77.1° 90° 102.9° 115.7° 128.6° 141.4° 154.3° 167.1° 180° | 2, 2, 7 | 2, 4, 7, 14, 28 |
| 29 | 12.4° | 14 | 12.4° 24.8° 37.2° 49.2° 62.1° 74.5° 86.9° 99.3° 111.7° 124.1° 136.6° | 29 | 29 |
| 30 | 12° | 15 | 12° 24° 36° 48° 60° 72° 84° 96° 108° 120° 132° 144° 156° 168° 180° | 2, 3, 5 | 2, 3, 5, 6, 10, 15, 30 |
| 31 | 11.6° | 15 | 11.6° 23.2° 34.8° 46.5° 58.1° 69.7° 81.3° 92.9° 104.5° 116.1° 127.7° 139.4° 151.0° 162.6° 174.2° | 31 | 31 |
| 32 | 11.3° | 16 | 11.3° 22.5° 33.8° 45° 56.3° 67.5° 78.8° 90° 101.3° 112.5° 123.8° 135° 146.3° 157.5° 168.8° 180° | 2, 2, 2, 2, 2 | 2, 4, 8, 16, 32 |
| 33 | 10.9° | 16 | 10.9° 21.8° 32.7° 43.6° 54.5° 65.5° 76.4° 87.3° 98.2° 109.1° 120° 130.9° 141.8° 152.7° 163.6° 174.5° | 3, 11 | 3, 11, 33 |
| 34 | 10.6° | 17 | 10.6° 21.2° 31.8° 42.4° 52.9° 63.5° 74.1° 84.7° 95.3° 105.9° 116.5° 127.1° 137.6° 148.2° 158.8° 169.4° 180° | 2, 17 | 2, 17, 34 |
| 35 | 10.3° | 17 | 10.3° 20.6° 30.9° 41.1° 51.4° 61.7° 72° 82.3° 92.6° 102.9° 113.1° 123.4° 133.7° 144° 154.3° 164.6° 174.9° | 5, 7 | 5, 7, 35 |
| 36 | 10° | 18 | 10° 20° 30° 40° 50° 60° 70° 80° 90° 100° 110° 120° 130° 140° 150° 160° 170° 180° | 2, 2, 3, 3 | 2, 3, 4, 6, 9, 12, 18, 36 |
| 37 | 9.7° | 18 | 9.7° 19.5° 29.2° 38.9° 48.6° 58.4° 68.1° 77.8° 87.6° 97.3° 107.0° 116.8° 126.5° 136.2° 145.9° 155.7° 165.4° 175.1° | 37 | 37 |
| 38 | 9.5° | 19 | 9.5° 18.9° 28.4° 37.9° 47.4° 56.8° 66.3° 75.8° 85.3° 94.7° 104.2° 113.7° 123.2° 132.6° 142.1° 151.6° 161.1° 170.5° 180° | 2, 19 | 2, 19, 38 |
| N, integer | (360/N)° | Number of Surfaces | All ∠° | Prime Factors | Symmetry Groups |
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