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.

Plan View of 36-Fold Symmetry Central Mogharnas DomePlan View of 36-Fold Symmetry Central Mogharnas DomeCreates a set of 18 unique muqarnas tiles

Plan View of 32-Fold Symmetry Central Mogharnas DomePlan View of 32-Fold Symmetry Central Mogharnas DomeCreates a set of 16 unique muqarnas tiles

Plan View of 14-Fold Symmetry Central Mogharnas DomePlan View of 14-Fold Symmetry Central Mogharnas DomeCreates a set of 7 unique muqarnas tiles

Plan View of 10-Fold Symmetry Central Mogharnas DomePlan View of 10-Fold Symmetry Central Mogharnas DomeCreates a set of 5 unique muqarnas tiles

Plan View of 8-Fold Symmetry Central Mogharnas DomePlan View of 8-Fold Symmetry Central Mogharnas DomeCreates a set of 4 unique muqarnas tiles

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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.
 
N, integer
 
(360/N)°
Number of
Surfaces
 
All ∠°
Prime
Factors
Symmetry
Groups
2180°1180°22
3120°1120°33
490°290° 180°2, 22, 4
572°272° 144°55
660°360° 120° 180°2, 32, 3, 6
751.4°351.4° 102.9° 154.3°77
845°445° 90° 135° 180°2, 2, 22, 4, 8
940°440° 80° 120° 160°3, 33, 9
1036°536° 72° 108° 144° 180°2, 52, 5, 10
1132.7°532.7° 65.5° 98.2° 130.9° 163.6°
1111
1230°630° 60° 90° 120° 150° 180°2, 2, 32, 3, 4, 6, 12
1327.7°627.7° 55.4° 83.1° 110.8° 138.7° 166.2°1313
1425.7°725.7°, 51.4°, 77.1°, 102.9°, 128.6°, 154.3°, 180°2, 72, 7, 14
1524°724° 48° 72° 96° 120° 144° 168°3, 53, 5, 15
1622.5°822.5° 45° 67.5° 90° 112.5° 135° 157.5° 180°2, 2, 2, 22, 4, 8, 16
1721.2°821.2° 42.4° 63.5° 84.7° 105.9° 127.1° 148.2° 169.4°1717
1820°920° 40° 60° 80° 100° 120° 140° 160° 180°2, 3, 32, 3, 6, 9, 18
1918.9°918.9° 37.9° 56.8° 75.8° 94.7° 113.7° 132.6° 151.6° 170.5°1919
2018°1018° 36° 54° 72° 90° 108° 126° 144° 162° 180°2, 2, 52, 4, 5, 10, 20
2117.1°1017.1° 34.3° 51.4° 68.6° 85.7° 102.9° 120° 137.1° 154.3° 171.4°3, 73, 7, 21
2216.4°1116.4° 32.7° 49.1° 65.5° 81.8° 98.2° 114.5° 130.9° 147.3° 163.6° 180°2, 112, 11, 22
2315.7°1115.7° 31.3° 47.0° 62.6° 78.3° 93.9° 109.6° 125.2° 140.9° 156.5° 172.2°2323
2415°1215° 30° 45° 60° 75° 90° 105° 120° 135° 150° 165° 180°2, 2, 2, 32, 3, 4, 6, 8, 12, 24
2514.4° 1214.4° 28.8° 43.2° 57.6° 72° 86.4° 100.8° 115.2° 129.6° 144° 158.4° 172.8°5, 55, 25
2613.8°1313.8° 27.7° 41.5° 55.4° 69.2° 83.1° 96.9° 110.8° 124.6° 138.5° 152.3° 166.2° 180°2, 132, 13, 26
2713.3°1313.3° 26.7° 40° 53.3° 66.7° 80° 93.3° 106.7° 120° 133.3° 146.7° 160° 173.3°3, 3, 33, 9, 27
2812.9°1412.9° 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, 72, 4, 7, 14, 28
2912.4°1412.4° 24.8° 37.2° 49.2° 62.1° 74.5° 86.9° 99.3° 111.7° 124.1° 136.6° 2929
3012°1512° 24° 36° 48° 60° 72° 84° 96° 108° 120° 132° 144° 156° 168° 180°2, 3, 52, 3, 5, 6, 10, 15, 30
3111.6°1511.6° 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°3131
3211.3°1611.3° 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, 22, 4, 8, 16, 32
3310.9°1610.9° 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, 113, 11, 33
3410.6°1710.6° 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, 172, 17, 34
3510.3°1710.3° 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, 75, 7, 35
3610°1810° 20° 30° 40° 50° 60° 70° 80° 90° 100° 110° 120° 130° 140° 150° 160° 170° 180°2, 2, 3, 32, 3, 4, 6, 9, 12, 18, 36
379.7°189.7° 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°3737
389.5°199.5° 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, 192, 19, 38
N, integer(360/N)°Number of
Surfaces
All ∠°Prime
Factors
Symmetry
Groups