# Octahedral Domes

Octahedral domes have their own unique symmetry patterns. You see squares in place of the familiar pentagons of icosahedral domes. These can be adapted for standard rectangle/square windows, skylights and doorways. Domes make nice greenhouses and shelters for many uses. With architectural development, larger domes can be fully functional economical earth friendly/user friendly homes or commercial buildings.

**Dome Termminology**

**Orientation:** Typical up-down axis for a convenient mid-point or hemisphere dividing line. This is the ‘normal’ Square Zenith orientation. This means the hemi-sphere ground perimeter (dome base) is flat for building on the ground/foundation. Other orientations are Face Zenith with triangle face at top, and Edge Zenith, with a strut (edge) at top. In some cases, the base perimeter struts are altered to make flat and level.

**Frequency:** Number of times the triangle face of the original polyhedron is divided into more triangles.

**Class:** Dividing lines are along those of the original polyhedra (Class I), or turned 90° (Class II). Class II types come in only even frequencies, 2, 4, 6 etc. See “Geodesic Math and How to Use It” by Hugh Kenner.

Octahedron and top half, divided in Class I two and three frequency grids

Octahedron 1 frequency, as a hub-strut pyramid

## OCTA-DOME 2 (2 frequency)

**Class I – three examples**

1. 4-way vertex at the top. Drawings show orthographic views- top, front, right side, and a pictorial see-thru wireframe. Colors are added to aid in visualization.

2. 6-way vertex at the top. This is the Octa Dome 2 HZ = Hexagon Zenith with a 6 sided base and a very nice and simple tall dome with unusual octa symmetry. Floor level cut-off might also be at the half way (hemi-sphere) point. Notice the vertical square areas front and back. Here doors and windows can be added, or more domes connected.

3. Equilateral triangle face at the top. This dome design has a regular hexagon for the base perimeter. To get an idea of the size potential, make a hexagon layout on the ground using 8 or 10 ft boards. Add a cupola top extension, Vertical Base Option, and subdividing struts. Refer to Cube – Octa Dome, Simplified Version

**Class II – two examples**

1. First example shows how it is equal to the Tetra-Dome. “Class” in dome terminology defines if the dome division is parallel to the underlying polyhedra or turned 90°. The Class II type are with divided triangles 90° from the octahedron. Please refer to the Tetra-Dome pages for more information.

2. Second example is the dome above turned 45° to produce an edge or strut at the top, the Edge Zenith (EZ). This is same as the Tetra-Dome EZ. It’s the best dome shape for simplicity, with only 10 Connectors and 21 struts needed, after the Icosa-Dome which has only 11 Connectors and 25 struts.

## OCTA-DOME 3 (3 frequency)

**Three Examples**

1. First is the 4 way vertex at the top (Square Zenith). This orientation gives central dividing line, a 1/2 geodesic = hemisphere dome.

We made a small Octa Dome 3 and made it our “Vine Dome“

2. Second is turned 45° to put a hexagon at top making the Hexagon Zenith (HZ). Floor level below the halfway point provides a nice dome with extra height (cutoff plane is lower than the hemisphere line).

3. The Edge Zenith (EZ) orientation with a strut at the dome top presents another interesting configuration. Floor level is even with the bottom struts of two opposite squares and provides another dome with extra height, near 5/8 fullness. Square area can be used to fit regular doors and windows, or openings large enough to drive in a vehicle – car, boat, RV – etc. This one could also be easily divided at the hemisphere for a shorter dome.

## Octa-Dome 4 (4 frequency)

**Class I – three examples**

1. First – “Normal” SZ oientation, with a level of triangles below the hemisphere used to add height (a Base Option) . Some of the bottom strut lines are modified to give a flat, horizontal ground level. Bottom triangles continue the dome’s roundness. Lower hexagons are vertical, making a good place to add a door

2. HZ – Hexagonal vertex is at the top. Similar to the Octa-Dome 3 above, the bottom squares are kept for a taller dome with more volume, and several lower struts (shown in blue) are altered for a flat base.

3. FZ – Face Zenith dome gives another interesting variation. The orientation provides a hemisphere for a 1/2 dome and a base with 12 sides.

The Double Dome concept demonstrated with this dome – Double Domes A study of the Octa-Dome 4 and the square/hex/face zenith orientations done with 3d surface shading.

**Class II – two examples**

1. SZ – Square Zenith with a 4-way vertex on top. As with previous examples the lower squares remain intact producing area below the half way point. Ground level struts (blue) are altered to give a flat base.

2. HZ – Orientation with a hexagon vertex on top. A geodesic hemisphere is produced which makes a convenient dividing line for a dome with a 12 sided base.

Octa-Domes such as shown above can make nice observatory domes with a convenient opening for telescope viewing. A fully rotate-able dome can be made by using grooved wheels attached to ground level Connector Hubs. The grooved wheels follow a round track that is the diameter of the bottom perimeter. Typical metal grooved wheels will support 300 lb. each which is more than enough for most small observatory domes. Please write for more details. See also: Observatory

## Octa-Dome 5 (5 frequency)

1. SZ – First example with a 4-way vertex on top.

2. Edge Zenith type with a strut at the top. Modified struts at the bottom provide for the flat ground perimeter.

## Octa-Dome 6 (6 frequency)

Class I dome, drawing of normal orientation with 4-way connection at top.

Octa-Domes are easily halved for convenient attachment to a vertical wall. Most orientations produce a cutting plane of struts that will produce a half dome or 1/4 sphere. Here a 6 frequency Class I dome as 1/4 sphere is shown. Colors show different types of struts. Each type has a particular length, angle, orientation on the dome and angle/orientation on its particular Connector Hub location. Photos of a 2 x 2 and 2 x 4 dome

The 1/4 dome (1/8 sphere) can be mounted against two vertical walls in a 90° corner.

1. Class II dome, drawing of normal (SZ) orientation with 4-way connection at top.

The Octa Dome 4 SZ is a four frequency octahedral dome with the square at top,shown above as a 20 ft diameter 2 x 4 dome with the Base Option, made from 2 x 4 wood.Four lower hexagon areas are vertical, making a good place to add a door and windows.More details here>> **with new 3D renderings.**

**Visit our Octa Dome page
and the
Cube-Octa dome
with it’s Simplified Version
the Rhombi-Cobe-Octa is another excellent octahedral based dome
and our “TR-CO” is the Truncated Cube-Octa Dome**