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This is computer aided drawing of rhombic dodecahedron
Working on possible shed geometry
Starting with 2 squares perpendicular,
first half diamond
first diamond of Rhombic dodecahedron
rotations of the diamond and formation of Rhombic dodecahedron
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This is drawing of first to last 2*4 ‘s locations of a 2V Geodesic Rhombic Dodecahedron
9 colors for 9 size/angles cuts
This is virtual framework of a Geodesic
Rhombic Dodecahedron
2V
On the Left is the Polyhedron’s front, side, top & bottom views!
The right. Is a component that the geodesic polyHedron is made of.
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These are rough Notes on sizes and angles of one piece of wood
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Working on possible shed geometry
Top
1-Starting with 2 squares perpendicular,
2-first half diamond
3-first diamond of Rhombic dodecahedron
4-5-6- rotations of the diamond and formation of Rhombic dodecahedron
Bottom
7-Transparent geodesic Rhombic Dodecahedron
8-Geodesic 2v Rhombic Dodecahedron
9- Top view of the shed
10- bottom view of the shed
11-front view
12- Perspective of the shed with door.
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I am practicing and learning Sketchup and eventually am trying to team up to do the real construction, I believe I can extract all the measurements of length and angles of the wood to be cut and so on…
Here trying to produce an Icosahedron
We start with 3 Golden Rectangles perpendicular, connecting all the corners we will come up with an Icosahedron
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So this is the first Icosahedral triangle,
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In these series of videos, next pages, I am showing some geometric rough notes of mathematically building different consecutive polyhedra from scratch, using conveniences of SketchUp
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In the video, the next page, the Icosahedron is already formed
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Icosahedron & Its component
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This is a 3 frequency Icosahedron; usually they divide the Edges of the triangles into 3 sections and project that onto the sphere, but i project the icosahedral triangle onto the sphere first, then divide every edge into 3 segments, this has advantages in certain types of construction, due to more number of equal edges
Icosahedral triangles are equilateral, so this dome consists of 20 X 9 = 180 triangles, and every 60 triangle is exactly identical
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3v honeYcomb icosahedron
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3 frequency Icosahedron, woodwork
Each of 6 colors (2x4) s are unique pieces of wood, hexahedrons with no 90’ angles
All The (2x4)s in this page are different irregular diamond and not a rectangular 2x4
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Managed to make a component, each of the six unique boards,
So edges and angles can be individually measured
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Working on a 4v icosahedron the woodwork (2x4s) on one triangle is ready, the component at the left is an actual component, which is repeated 60 times in the geodesic sphere
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In this
Video, the next page, the first pentagon is formed made of connecting the spikes merging out of the centers of the icosahedral triangles
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Here the pentagon derived from the icosahedron remains while the icosahedron is deleted, yet the three golden rectangle skeleton is still there.
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Here, in the next page, the pentagonal dodecahedron is forming using rotation in SketchUp
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Here the pentagonal dodecahedron is almost
done
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Architectural Geometry Exercise: Rhombicosidodecahedron By Tuğrul Yazar
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This is a Rombicosidodecahedron
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RhomBicosidodecahedron, is an icosahedron and a dodecahedron around it, both polyhedra have same edge, once we pull the faces of the polyhedra out they form this...
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Geodesic Rhombicosidodecahedron
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In the process to constructing a Pentagonal Dodecahedron base Geodome, using SketchUp
I have come up with a triangle component above to create the Geodesic structure
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This is a geodesic dodecahedron, it consists of 60 similar triangles and every corner resides on a single sphere, these are geodesic codes of strength
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This is a Pentakis Dodecahedron with
Wood-like frames...
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This is the Pentakis Dodecahedron with
Wood-like frames...
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This is a 2 frequency dodecahedron 60 repetitions of 4 unique triangles,
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Here every edge of the component has been devided into a five segment curve having all corners on a sphere this is going to be a 5 frequency dome
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Here i draw curves divided by 1, 2, 3, 4, 5 segment connecting 2 side curves which were divided into 5 segments
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The pentadome
5 frequency geodesic pentagonal dodecahedron;
It has 15 different sizes of triangles but they are close in size
25 X 60 = 1500 triangles total
The left and right small triangles within a bigger triangle, are equal in size but angles are “Opposites”. So in fact there maybe more variation of triangles depending on the constrution method
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This is Pentagonal Dodecahedron based Geodesic dome, each pentagon is divided into 5 triangles, each edge of such triangle is divided by 5 sections,
I have divided the edges projected onto the sphere, instead of dividing lines before projection, more uniformity is achieved this way, ofcourse this work for isosceles triangles
Penta-dome
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A pentagonal Dodecahedron, is ideal for a Geodesic Dome, because each pentagon can be divided into five triangles, and this makes 60 identical triangles to work with in construction,
This one is a 6 frequency, each edge of a triangle is divided into 6 sections,
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In the next video
I have
used the method
shown here:
to construct
the first golden rhombus of
the rhombic triacontahedron
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Here again, in the next page,
With the conveniences of the Sketchup I am building the rhombic triacontahedron,
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This hexagon on the rhombus of rhombic triacontahedron is the secret. Paul Robinson discovered to generate a new polyhedron (discovered in 2013)
Click: New Polyhedron discovery,
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Taking out extra lines
We come up with this
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Then this,
connecting the five corners
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Here, in the next page, the paulyheadron is completely constructed,
Attention that the component is not an actual component of the dome, it is only a component that worked for my sketchup project, in reality there are many overlaps of the faces which are not visible. An actual component for construction might not exist
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This is a new Polyhedron discovery, by Paul Robinson, I introduced the all triangle concept to it, Buckminster Fuller is for triangles because they hold shape better…
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We have all in triangles, next going to project all the corners of triangles onto a sphere, menwhile divide the hexagon and pentagon into 6 and 5 component triangles in SketchUp
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In the next page, i have divided every edge of the polygons into two, this is going to be a two frequency paulyheadron, yet now the polygons are flat
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THIS IS ALL TRIANGLES
ON SPHERE,
bUCKMINSTER FULLER PRINCIPLES OF STRENGTH
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In the next few pages, i gradually project the flat polygons onto a sphere by making the radius of the geodome exactly 70 feet
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It has 5 belts that the ground could be. …
Each color triangle is unique in size and angles
New BuckyBall,
I name it
PaulyHeadron,
2 frequency. Based on Paul Robinson’s
Near Rectified Truncated Rhombic Triacontahedron
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SIX FREQUENCY FLAT
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The orange is flat,
the light blue glass is curved
All curved
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One orange triangle has already curvrd up here, ,,,
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The penta is curved
the hex is flat
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This is a 6 frequency PAULYHEADRON 70 feet radius of the dome makes edges of triangles between 3 and 4 feet, ideal for wooden construction
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This is the only equilateral triangle, here which could be divided into three similar components
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This is same as page 47 only the green component being equilateral triangle has been divided into three components which saves time working with sketchup
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IN THE NEXT PAGES:
CREATION OF A RHOMBUS
(OF RHOMBIC dodecahedron)
Then creation of
the rhombic dodecahedron itself
Then the
“Near Rectified Truncated Rhombic dodecahedron”
This is imitation of Paul Robinson’s
“Near Rectified
Truncated Rhombic Triacontahedron”
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A Cube
Divided into 6 pyramids and the pyramids installed on the faces of that cube outward produces Rhombic dodecahedron, so the single rhombus is generated thus
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So a hexagon is drawn on each face of the Rhombic Dodecaheadron and connecting the Hexagons, we coe up with this near Rectified truncated rhombic dodecahedron
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near Rectified truncated rhombic dodecahedron
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GEODESIC NEAR RECTIFIED TRUNCATED RHOMBIC DODECAHEDRON
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THIS IS ALMOST A 2V GEODESIC NEAR RECTIFIED TRUNCATED RHOMBIC DODECAHEDRON
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THE 2 FREQUENCY GEODESC N.R.T.R.D.,
THE SQUARES ARE NOT CLASSIC 2V, BUT BEST FOR CONSTRUCTION
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THIS IS GEODESIC MODIFIED SOLID OF THE PREVIOUS PAGE, THE SQUARE HAS TURNED TO AN OCTAGON COULD BE A BRAND NEW POLYHEDRON
MayBe Colored glass ?
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THIS IS A HEXAKIS OCTAHEDRON, I STARTED WORKING ON IT BECAUSE IT IS BASICS OF A TIME MACINE OF MINE.
https://docs.google.com/presentation/d/1IZwlm_ggfzDNoFE2bwDActRFhZYI-mMcL-D-cz0ckis/edit?usp=sharing
DREW IRREGULAR HEXAGONS ON ALL 48 FACES OF THE POLYHEDRON, THEN: ELIMINATED THE REST OF THE SCULPTURE, THEN APPLIED THE GEODESIC PRINCIPLES, NEXT PAGE
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Hexakis Octahedron
Irregular geodesic Hexagons replacing rhe triangles
The corners are connected making squares and octagones
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THIS COULD BE ANOTHER NEW POLYHEDRON
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5 frequency Paulyheadron in progress
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Four frequency
Octahedron
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In this page you can see a cube divided into six pyramids, then mounted on the six faces of the cube, creating a Rhombic Dodecahedron
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This is a Geodesic Trunkadron
(truncated Rhomic dodecahedron)
In the next page, working on a house
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This is close to cubic patterns we are used to working, Geodesic Trunkadron is simplest for construction for it’s squares
Note that I have a basement...
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4 frequency Rhombic Dodecahedron
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Geodesic Rhombic Dodecahedron
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Half of Geodesic Rhombic Dodecahedron on the ground
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Half of Geodesic Rhombic Dodecahedron on the ground , with basement
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Truncated Rhombic Dodecahedron
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In this sketch I emphasized that the radius of the geodesic sphere be the distance of the center to a 3 edged corner?
Near
Truncated Rhombic Dodecahedron
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Near Truncated Rhombic Dodecahedron
Here the hexagons have equal edge lengths while having original Rhombic Dodecahedron angles
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Zomes
Easy Zome Drawing in Sketchup
Paul Robinson
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A
Rhombic Dodecahedron is a
Zome
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Zomes, construction with SketchUp,
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The geodesic 8 sided zome
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ZOMES 15 WITH BASEMENT OR UNDERWATER ...
BOTTOM VIEW
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CONVERSION OF A 21 SIDED zOME INTO A GEODESIC
SPHERE
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THIS IS A GEODESIC ZOME.
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This is the process of evolution of a cube, into a near truncated cube, I simply draw octagones on the faces of the cubes, this way we’ll have 8 similar triangles to work with
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Z0MES 12
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Geodesic near truncated
CUbe
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And finally the sphere turned to a house
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Geodesic truncated cuboctahedron
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Half grounded
Geodesic truncated cuboctahedron
Three main and two ground triangles
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A
shed design
Geodesic Truncated cuboctahedron
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This Is Geodesic pentagonal dodecahedron
The simplest geometry for a 12’ diameter
shed
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ThIs i drew for myself to park my moped winter nights It is sitting on 8 4*4s in concrete and has a little skirt like water protection mostly in the ground
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This is a basic framework of a geodesic pentagonal dodecahedron for a storage shed
A good idea but too much complication of base framework
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Bottom view
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71.3
3’ 8 ½”
108.9
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3’ 8 ½”
108.6
3’ 7 1/16”
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121.4
108.8
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This is the orange board measurements of the three board structure of geodesic pentagonal dodecahedron
3’ 6 1/16”
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This is Paul Robinson’s unity dome, next pages are DRawings for the purpos of building a storage shed
1-Tree golden rectangles perpendicular
2-two triangles of icosahedron
3-one fift of pentagon of dodecahedron
4-the split fifth for unity dome
5-symetric (twin) components of
the unity dome
next page
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6-geodesic pentagon
7-several pentagons put together
8-the complete dodecahedron
9-half of the geodesic sphere with it’s component
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10-this is a storage shed a “2V” Geodesic pentagonal dodecahedron
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Top
Side
bottom
Front
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The Basilica of Our Lady (Maastricht), whose enneahedron tower tops form a space-filling polyhedron.
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GEODESIC SHED RHOMBIC DODECAHEDRON
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Battle Shaft Armageddon
http://goo.gl/aedSZ
My father and the Christian Architects in Iran
http://goo.gl/yEyXr