Dome Geodesic Dome Geodesic Dome Notes & Calculator Geodesic Dome Diary Geodesic Polyhedra Polyhedra Notes Bow Dome Triangulated Bow Dome Star Dome Star Dome Diary Wigwam Zome Helix Zome Low Cost Dome (PVC) Miscellaneous Domes

Site Search

Enter term & press ENTER

If you found the information useful, consider to make a donation:

Page << Prev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | Next >>

# Geodesic Dome Notes & Calculator

written by Rene K. Mueller, Copyright (c) 2005, 2006, 2007, last updated Tue, January 29, 2019

## The Icosahedron

 Icosahedron
• Uniform Polyhedron: U22
• Platonic Solid
• Platonic Element: Water
• Vertices: 12
• Edges: 30
• Faces: 20
• Wythoff symbol: 5|2 3
• Symmetry Group: icosahedral
• Vertex Configuration: {3, 3, 3, 3, 3}
• Dual: dodecahedron
• V: s3 * 5/12 * (3 + √5)
• A: s2 * 20 / 4 * √3
• rinner: s / 12 * (3 * √3 + √15)
• router: s / 4 * √(10 + 2 * √5)

s = , V = , A = , rinner = , router = , ravg =

### 1V/L1 2/3 Icosahedron Dome

 Geodesic 1V 2/3 Icosahedron Dome (front view)
 Geodesic 1V 2/3 Icosahedron Dome (bird view)
• vertices/connectors: 11
• 5 x 4-way
• 6 x 5-way
•  1V 2/3 Icosahedron Dome Construction Map
• edges/struts & bending angles (αstrut):
• A x 25: 1.05146 (31.72°)
• faces: 15 (3-sided)
• A-A-A x 15 (60.00°, 60.00°, 60.00°)
• height: 1.447 or 72.36% of diameter

#### 1V 2/3 Icosahedron Dome Calculator

 Geodesic 1V 2/3 Icosahedron Dome (Human is 170cm/5'7")

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 25,
• h =

### 2V/L2 Icosahedron Dome

 Geodesic 2V Icosahedron Dome (front view)
 Geodesic 2V Icosahedron Dome (bird view)
• vertices/connectors: 26
• 10 x 4-way
• 6 x 5-way
• 10 x 6-way
•  2V Icosahedron Dome Construction Map
• edges/struts & bending angles (αstrut):
• A x 30: 0.54653 (15.86°)
• B x 35: 0.61803 (18.00°)
• total 65 struts (2 kinds)1)
• strut variance 13.1%
• faces: 40 (3-sided)
• A-A-B x 30 (55.57°, 55.57°, 68.86°)
• B-B-B x 10 (60.00°, 60.00°, 60.00°)
• 2 kinds of faces2)
• 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

#### 2V Icosahedron Dome Calculator

 Geodesic 2V Icosahedron Dome (Human is 170cm/5'7")

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 30,
• Blath = x 35,
• h =

Cut optimization:
• normalize Alath+Blath = 1.0, therefore Alath+Blath =
• cuts:
• 30 x (Alath+Blath):
• 5 x (Blath):
• total 35 laths to cut

### 3V 4/9 Icosahedron Dome

In some literature this variant is also called "3V 3/8 Dome".
 Geodesic 3V 4/9 Icosahedron Dome (front view)
 Geodesic 3V 4/9 Icosahedron Dome (bird view)
• vertices/connectors: 46
• 15 x 4-way
• 6 x 5-way
• 25 x 6-way
•  3V 4/9 Icosahedron Dome Construction Map
• edges/struts & bending angles (αstrut):
• A x 30: 0.34862 (10.04°)
• B x 40: 0.40355 (11.64°)
• C x 50: 0.41241 (11.90°)
• total 120 struts (3 kinds)1)
• strut variance 18.3%
• faces: 75 (3-sided)
• A-A-B x 30 (54.63°, 54.63°, 70.74°)
• B-C-C x 45 (58.59°, 60.70°, 60.70°)
• 2 kinds of faces2)
• height: 0.828 or 41.42% 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

#### 3V 4/9 Icosahedron Dome Calculator

 Geodesic 3V 4/9 Icosahedron Dome (Human is 170cm/5'7")

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 30,
• Blath = x 40,
• Clath = x 50,
• h =

Cut optimization:
• normalize Blath+Clath = 1.0, therefore Blath+Clath =
• cuts:
• 40 x (Blath+Clath):
• 10 x (Alath+Clath):
• 10 x (Alath+Alath):
• total 60 laths to cut

As you see the bottom isn't entirely even, for heavy construction you have to level them.

### 3V 5/9 Icosahedron Dome

In some literature this variant is also called "3V 5/8 Dome".
 Geodesic 3V 5/9 Icosahedron Dome (front view)
 Geodesic 3V 5/9 Icosahedron Dome (bird view)
• vertices/connectors: 61
• 15 x 4-way
• 6 x 5-way
• 40 x 6-way
•  3V 5/9 Icosahedron Dome Construction Map
• edges/struts & bending angles (αstrut):
• A x 30: 0.34862 (10.04°)
• B x 55: 0.40355 (11.64°)
• C x 80: 0.41241 (11.90°)
• total 165 struts (3 kinds)1)
• strut variance 18.3%
• faces: 105 (3-sided)
• A-A-B x 30 (54.63°, 54.63°, 70.74°)
• B-C-C x 75 (58.59°, 60.70°, 60.70°)
• 2 kinds of faces2)
• height: 1.188 or 59.38% 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

#### 3V 5/9 Icosahedron Dome Calculator

 Geodesic 3V 5/9 Icosahedron Dome (Human is 170cm/5'7")

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 30,
• Blath = x 55,
• Clath = x 80,
• h =

Cut optimization:
• normalize Blath+Clath = 1.0, therefore Blath+Clath =
• cuts:
• 55 x (Blath+Clath):
• 25 x (Alath+Clath):
• 3 x (Alath+Alath):
• total 83 laths to cut

As you see here as well that the bottom isn't entirely even, for heavy construction you have to level them.

### 4V Icosahedron Dome

 Geodesic 4V Icosahedron Dome (front view)
 Geodesic 4V Icosahedron Dome (bird view)
• vertices/connectors: 91
• 20 x 4-way
• 6 x 5-way
• 65 x 6-way
•  4V Icosahedron Dome Construction Map
• edges/struts & bending angles (αstrut):
• A x 30: 0.25318 (7.27°)
• B x 60: 0.29453 (8.47°)
• C x 30: 0.29524 (8.49°)
• D x 30: 0.29859 (8.59°)
• E x 70: 0.31287 (9.00°)
• F x 30: 0.32492 (9.35°)
• total 250 struts (6 kinds)1)
• strut variance 28.3%
• faces: 160 (3-sided)
• A-A-C x 30 (54.34°, 54.34°, 71.32°)
• B-B-C x 30 (59.92°, 59.92°, 60.16°)
• B-D-E x 60 (57.52°, 58.80°, 63.68°)
• E-E-F x 30 (58.72°, 58.72°, 62.55°)
• F-F-F x 10 (60.00°, 60.00°, 60.00°)
• 5 kinds of faces2)
• 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

#### 4V Icosahedron Dome Calculator

 Geodesic 4V Icosahedron Dome (Human is 170cm/5'7")

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 30,
• Blath = x 60,
• Clath = x 30,
• Dlath = x 30,
• Elath = x 70,
• Flath = x 30,
• h =

Cut optimization:
• normalize Elath+Elath = 1.0, therefore Elath+Elath =
• cuts:
• 60 x (Blath+Elath):
• 5 x (Elath+Elath):
• 30 x (Alath+Flath):
• 30 x (Clath+Dlath):
• total 125 laths to cut

The 4V looks very attractive, yet, I would recommend using the L3 version instead with less strut lengths and less strut variance.

### L3 Icosahedron Dome

 Geodesic L3 Icosahedron Dome (front view)
 Geodesic L3 Icosahedron Dome (bird view)
• vertices/connectors: 91
• 20 x 4-way
• 6 x 5-way
• 65 x 6-way
•  L3 Icosahedron Dome Construction Map
• edges/struts & bending angles (αstrut):
• A x 60: 0.27590 (7.93°)
• B x 60: 0.28547 (8.21°)
• C x 70: 0.31287 (9.00°)
• D x 30: 0.32124 (9.24°)
• E x 30: 0.32492 (9.35°)
• total 250 struts (5 kinds)1)
• strut variance 17.8%
• faces: 160 (3-sided)
• A-A-D x 30 (54.40°, 54.40°, 71.20°)
• A-B-C x 60 (54.68°, 57.60°, 67.72°)
• B-B-D x 30 (55.77°, 55.77°, 68.46°)
• C-C-E x 30 (58.72°, 58.72°, 62.55°)
• E-E-E x 10 (60.00°, 60.00°, 60.00°)
• 5 kinds of faces2)
• 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

#### L3 Icosahedron Dome Calculator

 Geodesic L3 Icosahedron Dome (Human is 170cm/5'7")

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 60,
• Blath = x 60,
• Clath = x 70,
• Dlath = x 30,
• Elath = x 30,
• h =

Cut optimization:
• normalize Clath+Clath = 1.0, therefore Clath+Clath =
• cuts:
• 60 x (Blath+Clath):
• 5 x (Clath+Clath):
• 30 x (Alath+Dlath):
• 30 x (Alath+Elath):
• total 125 laths to cut

The L3 might be a better choice for a 250 strut dome than the 4V variant: the L3 provides less strut variance 17.8% (5 kinds of struts) instead of 28.3% (6 kinds of struts).

Page << Prev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | Next >>

Content:

 Home · About · Tipi · Yurt · Dome · Features · Gallery

 Print · Bookmark

Creative Commons (CC) BY-SA-NC 2005-2017, developed, designed and written by René K. Müller
Graphics & illustrations made with Inkscape, Tgif, Gimp, PovRay, GD.pm