Lamp Basic Forms 2

A sampling of many possible volumes that can be used to create a lamp.
(NOTE: some, such as the tetrahedron, cube, and octahedron are generally too simple for the Lamp Project)

The volumes above are in three distinct categories:

The back row are Platonic solids, which contain repeated regular polygons. Thus, there is one repeated style of module in each.

- - Tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

With the exception of the second form, the middle row is made of volumes whose planes are regular polygons. There are two types of modules in each volume. The second form has two distinct modules, but one of them is not a regular polygon.
- - Cuboctahedron, cube with truncated edges, rhombicuboctahedron, truncated tetrahedron, icosadodecahedron, and truncated icosahedron.
The front row's volumes require only a single repeated module, however, these modules are not made from regular polygons.
1. - Rhombic dodecahedron, anti-stellated dodecahedron, stellated dodecahedron, and partially stellated icosadodecahedron.
2. In the case of the leftmost form, the module is not folded. Also, it is not made from equilateral triangles.
3. The other three contain modules that are folded along specific lines. These are necessary where planes meet at concave dihedral angles. Also, all of these are made from combinations of equilateral triangles and/or pentagons.
4. Notice that the second from the left also requires a glue tab. Glue tabs are necessary when making anti-stellated volumes.

Irregular Modules 1

Modules that make the forms in the front row of the rendering, matched to the rendered models.
From left to right: 12, 12, 30, and 12 modules would be needed.

Details

In relation to the Lamp Project, the Basic Volume is what creates a safe enclosure for the bulb, centers the bulb for even light distribution, and also forms the structure upon which extensions are designed. It is a polyhedron because it is made of polygons that meet at edges and vertices.

One Regular Polygonal Module

Regular Platonic polyhedra are one choice for lamps because their regular polygons are simple to draw, and each module is identical. As mentioned, only dodecahedrons and icosahedrons are acceptable because the others are too simple.

Two Or More Regular Polygonal Modules

Archimedean solids, Johnson solids, or other regular polyhedra are also excellent choices. There may be two or more different styles of modules. In some cases, this is beneficial for the Butterfly Problem when the polyhedron is made from two distinct polygons that is laid out so that now two alike modules join edges. This is the case with the icosadodecahedron: all triangle edges only touch pentagons, and all pentagonal edges only touch triangles.

Irregular Polygonal Modules

Stellated and anti-stellated polyhedra can also be employed, as seen in the image at the top of this page. When there are concave dihedral angles, simplify the modules by combining polygons and allowing for creases during assembly. Then the extensions only become necessary at convex dihedral angles. Further, you avoid having extensions face inwards, interfering with the light bulb.

In general, your basic volume must be clean and fully enclosed, made from planar material. Poorly fitted parts make the lamp feel messy, unrefined, and damaged.

Lastly, it is possible to make lamps from curved volumes, but this challenge requires your own research and testing, and also approval from the instructor.

More information for those interested:

For those that are statistics-minded, here are some polyhedra, with quantity of duplicate polygons, extensions, and other data:

Tetrahedron
- 4 equilateral triangles
- 4 vertices
- 6 dihedral angles
- 3 extensions per triangle
- 12 extensions overall
- Because there are only four modules, and the angles are very sharp, it is too simple for most lamps.
Cube (a dual of the octahedron)
- 6 perfect squares
- 8 vertices
- 12 dihedral angles
- 4 extensions per square
- 24 extensions overall
- Because there are only 6 modules and 90° angles, it is too simple for most lamps.
Octahedron (a dude of the cube)
- 8 equilateral triangles
- 6 vertices
- 12 dihedral angles
- 3 extensions per triangle
- 24 extensions overall
- Although there are 8 modules, it is too simple for many but the most clever lamps.
Dodecahedron (dual of the icosahedron)
- 12 regular pentagons
- 20 vertices
- 30 dihedral angles
- 5 extensions per pentagon
- 60 extensions overall
- 12 modules make for a good lamp.
Icosahedron (dual of the dodecahedron)
- 20 equilateral triangles
- 12 vertices
- 30 dihedral angles
- 3 extensions per triangle
- 60 extensions overall
- 20 modules make for a good lamp.
Truncated Tetrahedron
- 4 hexagons
- 4 triangles
- 12 vertices
- 18 dihedral angles (6 of one angle and 12 of another)
- 3 extensions per triangle and 4 extensions per square
- 36 extensions overall
- Because there are only 8 modules, this may be too simple for most lamps.
Cuboctahedron
- 8 equilateral triangles
- 6 perfect squares
- 12 vertices
- 24 dihedral angles
- 3 extensions per triangle and 4 extensions per square
- 48 extensions overall
- 14 modules of two types makes for a good lamp.
Rhombicuboctahedron
- 8 equilateral triangles
- 18 perfect squares
- 48 dihedral angles (24 of one type, and 24 of another)
- 3 extensions per triangle and 4 extensions per square
- 96 extensions overall
- 26 modules of two types makes for a good lamp.