26-Sided 16-Vertex Icosahexahedron Space Structure

Abstract

A Building Framework with 26 sides (Icosahexahedral) and 16 Vertices, known whimsically as a Silmaril. It is derived from the fusion of 2 Icosahedral Frameworks into a single framework with 3 equidistant and parallel internal planes, one plane a perfectly symmetrical 12 sided elliptical equatorial, the other 2 planes being geometrically related 6 sided inversions, resulting in useful practical applications of the Building Framework. Having 20 identical equilateral triangles, 2 sides which are isosceles triangles, another 2 sides different but geometrically related isosceles triangles, and 2 quadrilaterals again geometrically related to the previous triangles. It is geodesic in many planes resulting in great structural strength, integrity and aesthetic appearance. External alignment points allow joining multiple similar frameworks into expanded building frameworks in many dimensions. Some dimensions are of the Fibonacci Ratio. It aligns mystically in 2 dimensions perfectly with the Star Constellation Orion depicting an ancient Universal Sign of Peace.

1 . A Building Framework which is modular with 26 sides (Icosahexahedral) and 16 vertices which is a synthesis of two Icosahedral frameworks fused together retaining native vertices but also introducing new planes, with 3 internal planes which are parallel and equidistant, 2 which are 6-sided, the other 12-sided, where 20 sides are identical equilateral triangles, 2 sides are isosceles triangles, 2 sides are isosceles triangles with base equal to twice the base of the previous 2 triangles, and 2 sides are quadrilaterals allowing a perfect inclusion of 3 of the first 2 triangles alternatingly.  
     
     
         2 . The Double-Layer Shell Building Framework resulting from extruding outward of the sides of the Building Framework of  claim 1  giving thickness to the sides of the Building Framework by introducing struts of the length of the depth of the desired thickness perpendicular to the side planes of the Building Framework of  claim 1 , connected at the side vertices extruded out and subsequently connecting the resulting new strut ends to each closest new adjacent strut end resulting in essentially two Building Frameworks of  claim 1  of different dimensions one inside the other connected by interconnecting struts as defined by the inner Building and introducing gaps between sides in the outer layer shell which are defined in width by the depth of the shell.  
     
     
         3 . A Building Floor/Ceiling defined by either of the lower, upper, or central internal planes made up of either the central equatorial plane perfectly dissecting the Building Framework of  claim 1  about its natural vertex connections resulting in a 12 sided, elliptical floor/ceiling, or by either of the two different upper or lower planes defined by natural vertex connections of the Building Framework of  claim 1  which are equidistant to the central equatorial plane in opposite directions, both of which are different but are both 6 sided in inverse relation, and transform geometrically into each other through relationship with the equatorial plane of the Building Framework of  claim 1 .  
     
     
         4 . The 12 Sided, 6 End-Point Sided Tubular Sub-Building Framework created by removing the top and bottom caps from the Building Framework of  claim 1  which is a 6-sided ellipse at both ends but contains an alternating symmetrical transformational-correspondence from one end of the tube to the other, allowing adjacent tube frameworks to be connected along common interface points or edges by alternating each subsequent unit, extending the Tubular Framework into an indefinitely extendable articulated pipe with an alternating hexagonal cross-section, or extended vertically in a similar Building Framework to implement a building tower or stack.  
     
     
         5 . The Triangular (3-Sided) Tubular Longitudinal Sub-Building Framework of the Double-Layer Shell Framework of  claim 2  which are hollow or semi-hollow triangular beams resulting from the integration of struts connecting the inner and outer Building Frameworks of  claim 2  and all their inner and outer side edges.  
     
     
         6 . The Small Triangular Sub-Building Panel Units, which are sized to allow conventional orthogonal sized building materials to be placed within standard orthogonal stud dimensions but within the constraints of triangle shaped panels, 4 of which comprise larger Triangular Sub-building Panel Units and retain the orthogonal-to-triangular material mapping feature by extension, 4 of which joined correspond directly to the sides of the Building Framework of  claim 1 , are joined at the 3 corners without any special joining mechanism but rather by cutting one adjacent strut end at each corner in a 60 degree angle and connecting two struts at the corner together with a simple bolt or screw pattern that utilizes the 60 degree angle in making the joint.  
     
     
         7 . The Large Triangular Building Panel Units which correspond directly to the sides of the Building Framework of  claim 1 , which are made up of 4 of the Small Triangular Sub-Building Panel Units of  claim 6  joined together flush and parallel with a simple bolt or screw pattern, which are then joined at their inner edges to implement the Double-Layer Shell Building Framework of  claim 2 , by placing standard bolt or screw fasteners at the inner joint then an accompanying strut-work or blocking at the outer gap, the integration of which creates the Triangular Tubular Longitudinal Sub-Building Framework of  claim 5 .  
     
     
         8 . The Process of Constructing the Small Triangular Sub-Building Panel Units of  claim 6  without any special fasteners by using a standard bolt or screw method with the panel end points cut at a 60 degree angle to facilitate joining the end points together.  
     
     
         9 . The Process of Constructing the Large Triangular Sub-Building Units of  claim 7  where the Small Triangular Sub-building Panel Units of  claim 6  are joined together through a simple bolt or screw and plate pattern with the small units flush and adjacent together creating integrated beam structures internal to the Large Triangular Sub-Building Unit of  claim 7 .  
     
     
         10 . The Process of Constructing the Double-Layer Shell Building Framework of  claim 2  where the Large Triangular Sub-Building Panel Units of  claim 7  are joined first along one edge through a hinge method, where two adjacent panels are hinged at their inner edges together to facilitate rough placement of the two panels into their position in the Building Framework of  claim 2  as defined by the inner edges of the panels, where all subsequent Large Triangular Panels are hinged on one edge onto the placed units in the framework one edge at a time, in sequence, until the entire Building Framework is connected all along all inner edges by hinges allowing flexible adjustments to panel placements until all panels are finally properly placed comprising the Shell Building Framework of  claim 2 , whereupon final bolt or screw placements are done at the inner panel interfaces, then further strut-work or blocking is done at the outer interfaces with further bolt or screw placements to make the final unit connections, whereupon the hinges are then removed resulting in the Double-Layer Shell Framework of  claim 6  which is 2 Building Frameworks of  claim 1  one contained within the other but without final permanent bracing in the outer interfaces and a dimension gap between sides in the outer-layer Building Framework of  claim 1 .  
     
     
         11 . The Process of Construction where the gaps between adjacent joined panels of the sides of the Shell Building Framework of  claim 2  making up the Triangular Tubular Longitudinal hollow or semi-hollow beams of  claim 5  created by the depth between the inner and outer layers in the Shell Building Framework of  claim 2 , are filled with triangular supports (blocking) which fit the insertion angle of the triangular gap such that the base side of the isosceles triangular support faces in the direction of the outward extrusion making a semi-hollow beam, or instead, a single longitudinal brace is used to enclose the open end of the triangular hollow beam at the gap, into an enclosed triangular completely hollow beam which encloses the outer layer gaps between sides of the outer-layer of the Shell Building Framework of  claim 2 , making it a complete implementation of 2 Building Frameworks of  claim 1  contained within the other with the outer one expanded at the layer surface sides by the enclosed gap.  
     
     
         12 . The set of Concave Sub-Building Frameworks (trusses) with a minimum of 3 sides which result from dissecting the Shell Building Framework of  claim 2  across all possible adjacent edges, but excluding the Concave Building Sub-Framework of the set which is a 5 Sided Icosacap which is native to the Prior Art Icosahedron.  
     
     
         13 . The Building Framework resulting from removing the inner Building Framework of the Shell Building Framework of  claim 2  resulting in only the single outer layer framework retaining the extra connecting struts where their placement was defined by the original placement of the vertices of the inner Building Framework.  
     
     
         14 . The Building Framework of  claim 1  where strut sizes may deviate freely from the constraints of  claim 1  but still retain the same number of vertices in each side: 3 for any triangular side and 4 for any quadrilateral side, resulting in a freely non-symmetrical 26 Sided 16 Vertex Building Framework.  
     
     
         15 . The 26 Sided 15 Vertex Building Framework resulting from a transformation of the Building Framework of  claim 1  where the first 2 isosceles triangles are increased in size of the their base, then the second 2 isosceles triangles are decreased in size of their base, so that the first and second sets now are equal in base size, subsequently making the 2 quadrilaterals transform into the same equal triangles as they, as well such that the 20 identical equilateral triangles retain configuration as two fused Icosahedrons joined at interface points by the 6 newly transformed triangles, but no longer with the 3 internal parallel planes, whereby the two vertices previously connected by two edges of the connected quadrilaterals merge into one vertex, thereby reducing the vertex count of this Building Framework in still retaining the original 26 sides, but now has one less vertex to total 15 vertices.