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Triangulated Bow Dome

written by Rene K. Mueller, Copyright (c) 2007, last updated Sat, October 6, 2007

T. Bow Dome 45/0/6


Triangulated Bow Dome 45°/0°/6 (front view)

Triangulated Bow Dome 45°/0°/6 (bird view)

Triangulated Bow Dome 45°/0°/6 (top view)
  • vertices/connectors: 19
    • 6 x 4-way
    • 6 x 5-way
    • 7 x 6-way

  • Triangulated Bow Dome 45°/0°/6 Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 6: 0.44785 (12.94°)
    • B x 6: 0.54722 (15.88°)
    • C x 12: 0.56087 (16.29°)
    • D x 12: 0.66128 (19.31°)
    • E x 6: 0.83504 (24.68°)
    • F x 6: 1.00000 (30.00°)
    • total 48 struts (6 kinds)1)
    • strut variance 123.3%
  • faces: 30 (3-sided)
    • A-B-B x 6 (48.32°, 65.84°, 65.84°)
    • A-C-C x 6 (47.07°, 66.47°, 66.47°)
    • C-C-E x 6 (41.90°, 41.90°, 96.20°)
    • D-D-E x 6 (50.85°, 50.85°, 78.30°)
    • D-D-F x 6 (40.88°, 40.88°, 98.24°)
    • 5 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

T. Bow Dome 45/0/8


Triangulated Bow Dome 45°/0°/8 (front view)

Triangulated Bow Dome 45°/0°/8 (bird view)

Triangulated Bow Dome 45°/0°/8 (top view)
  • vertices/connectors: 29
    • 9 x 4-way
    • 4 x 5-way
    • 16 x 6-way

  • Triangulated Bow Dome 45°/0°/8 Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 4: 0.37211 (10.72°)
    • B x 4: 0.41871 (12.08°)
    • C x 16: 0.44394 (12.82°)
    • D x 4: 0.47413 (13.71°)
    • E x 8: 0.50447 (14.61°)
    • F x 8: 0.51760 (15.00°)
    • G x 16: 0.51882 (15.04°)
    • H x 8: 0.69145 (20.23°)
    • I x 8: 0.76537 (22.50°)
    • total 76 struts (9 kinds)1)
    • strut variance 105.7%
  • faces: 48 (3-sided)
    • A-E-F x 8 (42.67°, 66.78°, 70.54°)
    • B-B-D x 4 (55.52°, 55.52°, 68.97°)
    • C-C-E x 8 (55.37°, 55.37°, 69.26°)
    • C-C-H x 8 (38.84°, 38.84°, 102.32°)
    • D-F-F x 4 (54.51°, 62.74°, 62.74°)
    • G-G-H x 8 (48.21°, 48.21°, 83.59°)
    • G-G-I x 8 (42.47°, 42.47°, 95.07°)
    • 7 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

T. Bow Dome 45/0/10


Triangulated Bow Dome 45°/0°/10 (front view)

Triangulated Bow Dome 45°/0°/10 (bird view)

Triangulated Bow Dome 45°/0°/10 (top view)
  • vertices/connectors: 46
    • 10 x 4-way
    • 6 x 5-way
    • 30 x 6-way

  • Triangulated Bow Dome 45°/0°/10 Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 5: 0.30900 (8.89°)
    • B x 5: 0.31381 (9.03°)
    • C x 10: 0.33084 (9.52°)
    • D x 5: 0.33921 (9.76°)
    • E x 20: 0.34292 (9.87°)
    • F x 20: 0.36948 (10.65°)
    • G x 10: 0.38738 (11.17°)
    • H x 20: 0.42655 (12.31°)
    • I x 10: 0.47601 (13.77°)
    • J x 10: 0.57893 (16.83°)
    • K x 10: 0.61803 (18.00°)
    • total 125 struts (11 kinds)1)
    • strut variance 100.0%
  • faces: 80 (3-sided)
    • A-C-G x 10 (50.21°, 55.35°, 74.44°)
    • B-D-D x 5 (55.10°, 62.45°, 62.45°)
    • B-G-G x 5 (47.78°, 66.11°, 66.11°)
    • C-E-E x 10 (57.68°, 61.16°, 61.16°)
    • E-E-I x 10 (46.05°, 46.05°, 87.91°)
    • F-F-I x 10 (49.90°, 49.90°, 80.20°)
    • F-F-J x 10 (38.43°, 38.43°, 103.14°)
    • H-H-J x 10 (47.26°, 47.26°, 85.48°)
    • H-H-K x 10 (43.57°, 43.57°, 92.85°)
    • 9 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

T. Bow Dome 45/0/12


Triangulated Bow Dome 45°/0°/12 (front view)

Triangulated Bow Dome 45°/0°/12 (bird view)

Triangulated Bow Dome 45°/0°/12 (top view)
  • vertices/connectors: 61
    • 12 x 4-way
    • 12 x 5-way
    • 31 x 6-way
    • 6 x 7-way

  • Triangulated Bow Dome 45°/0°/12 Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 6: 0.22141 (6.36°)
    • B x 6: 0.24278 (6.97°)
    • C x 6: 0.28516 (8.20°)
    • D x 24: 0.29408 (8.46°)
    • E x 12: 0.30985 (8.91°)
    • F x 24: 0.31748 (9.13°)
    • G x 12: 0.34119 (9.82°)
    • H x 24: 0.36205 (10.43°)
    • I x 12: 0.37154 (10.71°)
    • J x 12: 0.43225 (12.48°)
    • K x 6: 0.44785 (12.94°)
    • L x 12: 0.49455 (14.32°)
    • M x 12: 0.51764 (15.00°)
    • total 168 struts (13 kinds)1)
    • strut variance 133.8%
  • faces: 108 (3-sided)
    • A-C-C x 6 (45.68°, 67.16°, 67.16°)
    • A-E-E x 6 (41.86°, 69.07°, 69.07°)
    • B-G-I x 12 (39.55°, 63.48°, 76.97°)
    • D-D-G x 12 (54.54°, 54.54°, 70.91°)
    • D-D-J x 12 (42.70°, 42.70°, 94.61°)
    • E-E-K x 6 (43.73°, 43.73°, 92.55°)
    • F-F-J x 12 (47.09°, 47.09°, 85.81°)
    • F-F-L x 12 (38.85°, 38.85°, 102.29°)
    • H-H-L x 12 (46.92°, 46.92°, 86.16°)
    • H-H-M x 12 (44.36°, 44.36°, 91.27°)
    • I-I-K x 6 (52.93°, 52.93°, 74.15°)
    • 11 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

T. Bow Dome 45/0/16


Triangulated Bow Dome 45°/0°/16 (front view)

Triangulated Bow Dome 45°/0°/16 (bird view)

Triangulated Bow Dome 45°/0°/16 (top view)
  • vertices/connectors: 109
    • 17 x 4-way
    • 8 x 5-way
    • 80 x 6-way
    • 4 x 7-way

  • Triangulated Bow Dome 45°/0°/16 Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 8: 0.19207 (5.51°)
    • B x 16: 0.19621 (5.63°)
    • C x 4: 0.20325 (5.83°)
    • D x 32: 0.21249 (6.10°)
    • E x 4: 0.21633 (6.21°)
    • F x 32: 0.21974 (6.31°)
    • G x 32: 0.23090 (6.63°)
    • H x 4: 0.23306 (6.69°)
    • I x 32: 0.24888 (7.15°)
    • J x 16: 0.25012 (7.18°)
    • K x 8: 0.25660 (7.37°)
    • L x 16: 0.25718 (7.39°)
    • M x 8: 0.27143 (7.80°)
    • N x 32: 0.27792 (7.99°)
    • O x 16: 0.31038 (8.93°)
    • P x 16: 0.35250 (10.15°)
    • Q x 16: 0.38021 (10.96°)
    • R x 16: 0.39018 (11.25°)
    • total 308 struts (18 kinds)1)
    • strut variance 103.1%
  • faces: 200 (3-sided)
    • A-B-J x 16 (49.19°, 50.62°, 80.19°)
    • B-D-D x 16 (54.99°, 62.51°, 62.51°)
    • C-K-M x 8 (45.16°, 63.56°, 71.28°)
    • D-D-L x 16 (52.76°, 52.76°, 74.48°)
    • E-E-H x 4 (57.40°, 57.40°, 65.21°)
    • F-F-L x 16 (54.17°, 54.17°, 71.65°)
    • F-F-O x 16 (45.06°, 45.06°, 89.89°)
    • G-G-O x 16 (47.77°, 47.77°, 84.47°)
    • G-G-P x 16 (40.24°, 40.24°, 99.52°)
    • H-M-M x 4 (50.86°, 64.57°, 64.57°)
    • I-I-P x 16 (44.92°, 44.92°, 90.16°)
    • I-I-Q x 16 (40.20°, 40.20°, 99.59°)
    • J-J-K x 8 (59.14°, 59.14°, 61.73°)
    • N-N-Q x 16 (46.84°, 46.84°, 86.32°)
    • N-N-R x 16 (45.41°, 45.41°, 89.18°)
    • 15 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

T. Bow Dome 45/0/20


Triangulated Bow Dome 45°/0°/20 (front view)

Triangulated Bow Dome 45°/0°/20 (bird view)

Triangulated Bow Dome 45°/0°/20 (top view)
  • vertices/connectors: 166
    • 20 x 4-way
    • 16 x 5-way
    • 120 x 6-way
    • 10 x 7-way

  • Triangulated Bow Dome 45°/0°/20 Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 10: 0.15089 (4.33°)
    • B x 5: 0.15413 (4.42°)
    • C x 10: 0.16498 (4.73°)
    • D x 5: 0.16542 (4.74°)
    • E x 20: 0.16748 (4.80°)
    • F x 40: 0.17073 (4.90°)
    • G x 5: 0.17432 (5.00°)
    • H x 40: 0.17536 (5.03°)
    • I x 40: 0.18186 (5.22°)
    • J x 20: 0.18852 (5.41°)
    • K x 40: 0.19129 (5.49°)
    • L x 10: 0.20182 (5.79°)
    • M x 40: 0.20522 (5.89°)
    • N x 20: 0.20622 (5.92°)
    • O x 20: 0.20951 (6.01°)
    • P x 40: 0.22549 (6.47°)
    • Q x 20: 0.24097 (6.92°)
    • R x 10: 0.24915 (7.16°)
    • S x 20: 0.27038 (7.77°)
    • T x 20: 0.29308 (8.43°)
    • U x 20: 0.30769 (8.85°)
    • V x 20: 0.31287 (9.00°)
    • total 475 struts (22 kinds)1)
    • strut variance 107.4%
  • faces: 310 (3-sided)
    • A-E-O x 20 (45.52°, 52.37°, 82.11°)
    • B-G-G x 5 (52.47°, 63.77°, 63.77°)
    • B-L-L x 5 (44.89°, 67.55°, 67.55°)
    • C-D-L x 10 (52.26°, 52.44°, 75.29°)
    • C-J-J x 10 (51.91°, 64.05°, 64.05°)
    • E-F-F x 20 (58.76°, 60.62°, 60.62°)
    • F-F-N x 20 (52.84°, 52.84°, 74.31°)
    • H-H-N x 20 (54.00°, 54.00°, 72.00°)
    • H-H-Q x 20 (46.61°, 46.61°, 86.79°)
    • I-I-Q x 20 (48.51°, 48.51°, 82.97°)
    • I-I-S x 20 (41.99°, 41.99°, 96.02°)
    • J-J-R x 10 (48.62°, 48.62°, 82.75°)
    • K-K-S x 20 (45.03°, 45.03°, 89.94°)
    • K-K-T x 20 (40.00°, 40.00°, 100.01°)
    • M-M-T x 20 (44.42°, 44.42°, 91.15°)
    • M-M-U x 20 (41.43°, 41.43°, 97.14°)
    • O-O-R x 10 (53.51°, 53.51°, 72.99°)
    • P-P-U x 20 (46.98°, 46.98°, 86.04°)
    • P-P-V x 20 (46.07°, 46.07°, 87.86°)
    • 19 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

For truly bow based approach, without triangulation, see Bow Dome which also includes canvas calculator which could be used to cover the triangulated approach.


(End of Article)

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