# List of Possible Patents

No. | Patent | Independent Invention | Date | Dependent Inventions | Date |
---|---|---|---|---|---|

1 | Modified Rhombic Triacontahedron Truss | MRT Truss | 2005-09-18 | - | - |

2 | Equilateral Triangular Truss | Equilateral Triangle Truss | 2011-06-20 | Covering Isocelese Areas with ET Truss | 2011-06-20 |

3 | Modified Rhombic Triacontahedron Domes | Modified Rhombic Triacontahedron | 2005-09-18 | Modified Rhombic Triacontahedron With Central Bracing (Note: Make this to compare with MRT.) | 2011-05-12 |

Modified Rhombic Triacontahedron With Central Diamond Bracing | 2011-05-12 | ||||

Modified Rhombic Triacontahedron (Three Quadrilaterals) (Note: Calculate Equal area data also.) | 2011-05-12 | ||||

Modified Rhombic Triacontahedron (Eight Triangles) | 2011-05-12 | ||||

Modified Rhombic Triacontahedron (Eight Triangles plus a quadrilateral) (Note: Calculate equal area variation.) | 2011-05-12 | ||||

4 | Higher Frequencies Modified Rhombic Tricontrahedron Domes | Two frequency MRT ( Sub division by Side) Typed Version also exists | 2008-02-11 | ||

6 | Three Frequency Octahedron Subdivisions With Equal Deficit Angle (Side subdivision) No Length Calculations attached | No | - | ||

7 | Three Frequency Iscoshedron Subdivisions With Equal Deficit Angle (Side subdivision) No Calculations attached | - | - | ||

8 | Eight Panel Sphere (Non Geodesic Dome composed of 4 primary quarters Split into 7 panels each) Non Equal Deficit Angle | No | - | ||

9 | Method of Generating stuructures with equal deficit angles. (Not documented) | Yes | 2005-09-18 | ||

10 | Two frequency Icosahedron (three quadrilaterals) | Yes | 2011-06-06 | ||

11 | Four Frequency Icosahedron (nine quadrilaterals) | No | 2011-06-07 | ||

12 | Four Frequency Icosahedron (twelve quadrilaterals) | No | 2011-06-07 | ||

13 | Two frequency MRT (Eight quadrilaterals) | No | 2011-05-30 | ||

14 | Three Frequency MRT (Nine Quadrilaterals) | No | 2011-05-30 | ||

15 | Three Frequency MRT (Eight Quadrilaterals plus One Rectangle) | No | 2011-05-30 | ||

21 | Two frequency MRT ( Seven quadrilaterals) | No | 2011-05-29 | ||

24 | Four Frequncy MRT (482 verticies) | No | TBD |

No. | Title of Invention | Independent (Yes / No) | Date |
---|---|---|---|

1 | Modified Rhombic Triacontahedron | Yes | 2005-09-18 |

2 | MRT Truss | Yes | 2005-09-18 |

3 | Eight Panel Sphere (Non Geodesic Dome composed of 4 primary quarters Split into 7 panels each) | No | 2008-01-18 |

4 | Three Frequency Iscoshedron Subdivisions With Equal Deficit Angle (Side subdivision) | No | 2008-01-19 |

5 | Two frequency MRT ( Sub division by Side) Typed Version also exists | No | 2008-02-11 |

6 | Three Frequency Octahedron Subdivisions With Equal Deficit Angle (Side subdivision) No Length Calculations attached | No | - |

7 | Three Frequency Iscoshedron Subdivisions With Equal Deficit Angle (Side subdivision) No Calculations attached | - | - |

8 | Eight Panel Sphere (Non Geodesic Dome composed of 4 primary quarters Split into 7 panels each) Non Equal Deficit Angle | No | - |

9 | Method of Generating stuructures with equal deficit angles. (Not documented) | Yes | 2005-09-18 |

10 | Two frequency Icosahedron (three quadrilaterals) | Yes | 2011-06-06 |

11 | Four Frequency Icosahedron (nine quadrilaterals) | No | 2011-06-07 |

12 | Four Frequency Icosahedron (twelve quadrilaterals) | No | 2011-06-07 |

13 | Two frequency MRT (Eight quadrilaterals) | No | 2011-05-30 |

14 | Three Frequency MRT (Nine Quadrilaterals) | No | 2011-05-30 |

15 | Three Frequency MRT (Eight Quadrilaterals plus One Rectangle) | No | 2011-05-30 |

16 | Modified Rhombic Triacontahedron With Central Bracing (Note: Make this to compare with MRT.) | No | 2011-05-12 |

17 | Modified Rhombic Triacontahedron With Central Diamond Bracing | No | 2011-05-12 |

18 | Modified Rhombic Triacontahedron (Three Quadrilaterals) (Note: Calculate Equal area data also.) | No | 2011-05-12 |

19 | Modified Rhombic Triacontahedron (Eight Triangles) | No | 2011-05-12 |

20 | Modified Rhombic Triacontahedron (Eight Triangles plus a quadrilateral) (Note: Calculate equal area variation.) | No | 2011-05-12 |

21 | Two frequency MRT ( Seven quadrilaterals) | No | 2011-05-29 |

22 | Equilateral Triangle Truss | Yes | 2011-06-20 |

23 | Covering Isocelese Areas with ET Truss | No | 2011-06-20 |

24 | Four Frequncy MRT (482 verticies) | No | TBD |

## 1. Modified Rhombic Tricontrahedron Truss (MRTT)

The Octet truss as well as other Space Frames occupy a plane and do not lend themselves to making of geodesic domal structures. Large domes cannot be generated out of simple platonic solids as their strut lengths are limited by the material used to generate a panel. Consequently, large domes are built by repeatedly sub-dividing the platonic faces (or any other geometry that is chosen) and extending the new vertices to the spherical surfaces. Such sub-divided adjacent faces (that can be constructed out of conventional material) meet at dihedral angles, and two or more adjacent faces cannot be in one plane. The Modified Rhombic Tricontrahedron Truss (MRTT) is designed to generate geodesic domes with a radius that is as large as desired, using conventional materials. This is done by making individual panels with repeating trusses so that the size of each panel is not restricted in any significant manner by the choice of material with which the panel is built. This allows a MRTT geodesic dome to be built of trussed panels of un-sub-divided faces. In addition, the generated dome is aesthetically superior to others generated by conventional geometries. MRTT is so designed that it can also be put to other conventional uses of space frames.

## 2. Equilateral Triangular Truss (ETT)

The Octet truss as well as other Space Frames occupy a plane and do not lend themselves to making of geodesic domal structures. Large domes cannot be generated out of simple platonic solids as their strut lengths are limited by the material used to generate a panel. Consequently, large domes are built by repeatedly sub-dividing the platonic faces (or any other geometry that is chosen) and extending the new vertices to the spherical surfaces. Such sub-divided adjacent faces (that can be constructed out of conventional material) meet at dihedral angles, and two or more adjacent faces cannot be in one plane. The Equilateral Triangular Truss is designed to generate a geodesic dome with a radius as large as desired, using conventional materials. This is done by making individual panels with repeating trusses so that the size of each panel is not restricted in any significant manner by the choice of material with which the panel is built. The panels have to be Equilateral angular in shape, which limits the domes to Tetrahedral, Octahedral or Icosahedral geometries with 1 frequency. This allows an ETT geodesic dome to be built of trussed panels of unlimited size with 1 frequency. Prior Art generates domes by sub-dividing platonic solids like Tetrahedron, Octahedron or Icosahedron into 2 or more frequency sub divisions. Such subdivisions are largely composed of scalene and isosceles triangles with a few equilateral triangles in the center. The patent discloses (or a separate patent will disclose) a method of covering scalene triangles or isosceles triangles with Equilateral Triangular Trusses so that domes that are composed of such triangles can also be built with as-large-as-desired radius with conventional material.

## 3. Modified Rhombic Tricontrahedron Domes

Prior Art discloses Geodesic Domes that have been generated by sub-dividing Platonic solid faces. Tetrahedron, Octahedron, and Icosahedron are three Platonic solids that have four, eight and twenty faces that are identical and available for the geodesic sub-divisions. Rhombic Tricontrahedron is not a Platonic solid. Nevertheless Fuller in his patent, 9999999 disclosed its uses for generating geodesic (or near geodesic) structures. The rhombic tricontrahedron has 12 vertices of icosahedron and twenty vertices of Dodecahedron that are on two different spheres of nearly the same radius. Fuller patent discloses, without giving any reasons for it, that the twenty vertices that are from Dodecahedron were physically removed from the structure by Fuller and were replaced by holes with chains encircling the holes. The inventor believes that these holes constitute local points of structural weaknesses. The Modified Rhombic Tricontrahedron (MRT) is an innovation structure disclosed in the patent that has no local points of weakness. All its vertices have the same deficit angles and lie on a sphere. Domes built of MRT have superior aesthetic value compared to all other prior art domes. The fabrication of MRT domes is cheaper as they involve fewer parts than Prior Art domes.

## 4. Method Of Generating Geodesic/ Near Geodesic Structures With Equal Deficit Angles.

Historically, Geodesic structures began by focusing on Geodesics that can be drawn on the surfaces of a sphere. Fuller found ways to locate vertices (hubs) such that they were drawn on a geodesic and the struts were chords of the geodesic. Later, geodesic structures were shown to be a special case of tensegrity structures where compression and tension were balanced and there were no redundant parts. Hugh Kenner’s book “Geodesic Maths And How To Use It” clearly pointed out that tensegrity structures could follow any geometry and were in no way tied to spheres. Dick Fischenbeck's patent, which discloses a way to place the vertices in a random manner so that no regular geometry at all is followed, is a vindication of Hugh Kenner's insight. René Descartes, a mathematician (1596-1650), found that the sum of the angular deficits of all the vertices of a closed convex body is equal to 720°. Prior art discloses several methods of generating geodesic structures that are commonly called Class I or Class II or Class III that can be combined with Method 1 or Method 2. The patent discloses a novel method of generating geodesic structures/near-geodesic structures that dispenses with beginning the process with any platonic solid or any regular geometry. The generated structures are such that they have equal angular deficit at each vertex; there are no local points of weaknesses in them and they are aesthetically very pleasing. The novel method can also generate near geodesic structures with desired numbers of angular deficits at vertices.

## 5. Icosahedral Domes Sub-Divided To Yield Equal Deficit Angles

Prior art discloses several methods of generating geodesic structures that are commonly called Class I or Class II or Class III that can be combined with Method 1 or Method 2. Hugh Kenner’s book “Geodesic Maths And How To Use It” is one often referred source of prior art. Most of the domes that have been actually constructed follow a 3 frequency sub-division of an icosahedron. Icosahedron are prior art preferred geometry because the twenty faces of an icosahedron need only a few sub-divisions (as compared to larger sub-divisions of Octahedron or even larger sub-division of tetrahedrons) to yield satisfactory domal structures. Icosahedral sub-divisions yield scalene, isosceles, and equilateral triangles. If sides of a triangle are known, mathematical formula will quickly yield the values of angles between the sides. Many prior art sources thus report only the chord lengths of the triangles that constitute the sub-division. See, for instance, the well-known Dome Calculator at http://www.desertdomes.com/domecalc.html Other sites like Simply Different (http://www.simplydifferently.org/) also give the angles between the sides. When the angles that are between the chords that are meeting at a vertex (hub) are known, the angular deficit at that vertex is simply three sixty degrees minus the sum of all the angles between the chords that are meeting at that vertex. Prior art discloses no sub-division of an Icosahedron by different Classes and Methods wherein the angular deficit is equal at all the vertices. The patent discloses several sub-divisions of an Icosahedron wherein the angular deficit is equal at all the vertices. The Icosahedra sub-divisions have no local points of failure and are aesthetically pleasing.

## 6. Octahedral Domes Sub-Divided To Yield Equal Deficit Angles

Prior art discloses several methods of generating geodesic structures that are commonly called Class I or Class II or Class III that can be combined with Method 1 or Method 2. Hugh Kenner’s book “Geodesic Maths And How To Use It” is one often referred source of prior art. Most of the domes that have been actually constructed follow a 3 frequency sub-division of an icosahedron. However a few domes do follow Octahedral sub-divisions of four or higher frequencies. Using Octahedral sub -divisions allows nearly rectangular openings to be incorporated in the dome in a natural manner. Octahedral sub-divisions yield scalene, isosceles, and equilateral triangles. If the sides of a triangle are known, mathematical formula will quickly yield the values of angles between the sides. Many prior art sources thus report only the chord lengths of the triangles that constitute the sub-division. The well-known Dome Calculator at http://www.desertdomes.com/domecalc.html does not give any data for Octahedral domes. However, Simply Different (http://www.simplydifferently.org/) gives both the chord factors and the angles between the sides for Octahedral domes of different frequencies. When the angles that are between the chords that are meeting at a vertex (hub) are known, the angular deficit at that vertex is simply three sixty degrees minus the sum of all the angles between the chords that are meeting at that vertex. Prior art discloses no sub-division of an Octahedron by different Classes and Methods wherein the angular deficit is equal at all the vertices. The patent discloses several sub-divisions of an Octahedron wherein the angular deficit is equal at all the vertices. The Octahedral sub-divisions have no local points of failure and are aesthetically pleasing.

## 7. Higher Frequencies Modified Rhombic Tricontrahedron Domes

Modified Rhombic Tricontrahedron is a structure that can be used to make geodesic domes that are limited in their radius by the strength of the material used to construct them. When domes of large diameters are required, sub-divisions of the Modified Rhombic Tricontrahedron are to be used. Prior art does not disclose any method of sub-division directly rendered on a Modified Rhombic Tricontrahedron. However, it may be possible to extend the Classes and methods of sub-dividing Icosahedrons and Octahedrons to cover the MRT also. By the very nature of such prior art sub-divisions the newly generated sub-divisions will not have equal angular deficits at all the vertices (hubs). The patent discloses novel ways of generating higher frequencies MRT sub-divisions such that all the vertices have equal angular deficits. The MRT sub-divisions have no local points of failure and are aesthetically pleasing. Additionally, the patent discloses methods of incorporating near rectangular openings /other architecturally desirable artifacts in higher frequency MRT.

## 8. Rectangular Geodesic Structures

Geodesic structures are usually constructed with a circular floor plan. Prior art, including Hugh Kenner's book “ Geodesic Math and How to Use It” discloses several methods by which the circular floor plan may be replaced by an elliptical door plan. It also discloses methods of divorcing the eccentricity of the elliptical floor plan from the eccentricity of the overhead structure. Such ellipsoidal geodesic structures require very large amount of calculations for the huge number of chord factors that they contain. John Zerning’s web site discloses a way of covering rectangular areas (http://www.johnzerning.com/category/ellipsoid/) with ellipsoidal geodesics as well as non-geodesic structures (http://www.johnzerning.com/category/barrel-vault/). It discloses ways to cover other areas also (http://www.johnzerning.com/category/hexagonal/) The patent discloses a novel way of covering rectangular areas with geodesic structures/ near-geodesic structures such that almost all the area of the rectangle is covered with very little wastage and limited amount of computation. NB: Though the subject matter could be immediately submitted for a patent I am still trying to improve the solution. This is one patent that has immediate applications in India (whole of developing world for Green House Agriculture) yet I do not see how I can actually enforce the patent?

## 9. Babushka Dolls Geodesic Structures

Prior art in geodesic domes mostly stops at generating the elements of the domal structure. As most domes that are fabricated are relatively small in diameter, the interior of the dome gets populated with conventional civil structures to yield a basement, a ground floor and an attic type structure at the top. The Montreal Expo Dome was 250 feet in diameter and 200 feet in height. It had no worthwhile internal structure. Eden dome, far bigger in size, in London is used as a biosphere and is structurally empty. In prior art disclosed by Fuller, a design of a textile mill that spirals along the edge of the dome has been delineated. In other prior art by Fuller a Geodesic dome with a radius of half a mile that encloses a city under it has been delineated. There is no internal structure that has been disclosed. In still other prior art by Fuller, a covered geodesic dome that is covered with fabric so that it can retain internal heat and has a radius of over half a mile so that it can float freely in the air without any fuel consumption has been delineated. There is no internal structure that has been disclosed. The patent discloses several methods of populating large domal structures such that the outermost geodesic structure houses underneath it another geodesic structure and that geodesic structure houses another geodesic structure underneath it, and so on, as the designer desires. The patent discloses several alternate methods of connecting the various geodesic structures. The patent discloses several alternate methods of controlling light and air in the overall structure to suit the needs of its inhabitants.