###### A Non-Regular Icosahedron Geometry Satellite Form, Mirror Invested Polyhedro Heliotrope, For Optical

Working on relationships of three circles in common ratio [4/π or square root of the golden number ] and drawing lines of related tangents,

squares and triangles, viewed on the paper plan, a figure having the shape of a section [Hexagonal] similar to that of an Icosahedron

or Dodecahedron. This gave me the idea of searching for an existing probable Polyhedron built upon this traced shape. In fact this

Polyhedron was built[ 4x scale], whose geometry relates to the Icosahedron and the Dodecahedron. It is a non regular Icosahedron

having 12 Isosceli triangles and 8 Equilateral triangles. Mirror triangles cut to size, invested the structure for the configuration of a

“Polyhedroheliotrope”Satellite Optical Tracking application.

This work is part [mainly geometric configurations’ presentation] of my published book :Treatise on Circle Generator Polyhedron

Harmony and Disharmony Condition of Three Concentric Circles in Common Ratio, ISBN978 – 618 – 83169 – 0 - 4, National Library

of Greece 04/05/2017 by Panagiotis Ch. Stefanides.“Generator” refers to the geometric characteristics of this Solid found to be roots of

the other Solid Polyhedra i.e. Platonic/Eucleidean Solids.

Adv Theo Comp Phy, 2019

ISSN: 2639-0108

www.opastonline.com

Figure 2: Skeleton Parallelogramme Planes’ Co-ordinates’ Definition and 3D AutoCAD Design Geometry and Vector

Co-ordinates’ Definition By Panagiotis Stefanides - AutoCad Computation By Dr. Giannis Kandylas

Figure 1: Polyhedron Parallelogramme Planes’ Corners’ Lines Joined and 3D AutoCAD Design Geometry and Vector

Co-ordinates’ Definition By Panagiotis Stefanides - AutoCad Computation By Dr. Giannis Kandylas

Adv Theo Comp Phy, 2019 Volume 2 | Issue 2 | 2 of 8

Figure 3: “Generator Polyhedron” Paper Structure and Mirrors’ Invested

Figure 4: “Generator Polyhedron” Skeleton Paper Structure [ left], Dark Chamber Simulation of Polyhedroheliotrope” Satellite Optical

Tracking right]

2a: Polyhedron Geometry Based on a Special Triangle Involving the SQUARE ROOT OF THE GOLDEN SECTION

[ ArcTan (1.27201965..) = 51.8272 9238 Deg].

Triangle Interpretation by Panagiotis Stefanides from Plato’s Timaeus.

Figure 5a: Plato’s Timaeus “Most Beautiful Triangle. Interpretation By Panagiotis Stefanides

squares and triangles, viewed on the paper plan, a figure having the shape of a section [Hexagonal] similar to that of an Icosahedron

or Dodecahedron. This gave me the idea of searching for an existing probable Polyhedron built upon this traced shape. In fact this

Polyhedron was built[ 4x scale], whose geometry relates to the Icosahedron and the Dodecahedron. It is a non regular Icosahedron

having 12 Isosceli triangles and 8 Equilateral triangles. Mirror triangles cut to size, invested the structure for the configuration of a

“Polyhedroheliotrope”Satellite Optical Tracking application.

This work is part [mainly geometric configurations’ presentation] of my published book :Treatise on Circle Generator Polyhedron

Harmony and Disharmony Condition of Three Concentric Circles in Common Ratio, ISBN978 – 618 – 83169 – 0 - 4, National Library

of Greece 04/05/2017 by Panagiotis Ch. Stefanides.“Generator” refers to the geometric characteristics of this Solid found to be roots of

the other Solid Polyhedra i.e. Platonic/Eucleidean Solids.

Adv Theo Comp Phy, 2019

ISSN: 2639-0108

www.opastonline.com

Figure 2: Skeleton Parallelogramme Planes’ Co-ordinates’ Definition and 3D AutoCAD Design Geometry and Vector

Co-ordinates’ Definition By Panagiotis Stefanides - AutoCad Computation By Dr. Giannis Kandylas

Figure 1: Polyhedron Parallelogramme Planes’ Corners’ Lines Joined and 3D AutoCAD Design Geometry and Vector

Co-ordinates’ Definition By Panagiotis Stefanides - AutoCad Computation By Dr. Giannis Kandylas

Adv Theo Comp Phy, 2019 Volume 2 | Issue 2 | 2 of 8

Figure 3: “Generator Polyhedron” Paper Structure and Mirrors’ Invested

Figure 4: “Generator Polyhedron” Skeleton Paper Structure [ left], Dark Chamber Simulation of Polyhedroheliotrope” Satellite Optical

Tracking right]

2a: Polyhedron Geometry Based on a Special Triangle Involving the SQUARE ROOT OF THE GOLDEN SECTION

[ ArcTan (1.27201965..) = 51.8272 9238 Deg].

Triangle Interpretation by Panagiotis Stefanides from Plato’s Timaeus.

Figure 5a: Plato’s Timaeus “Most Beautiful Triangle. Interpretation By Panagiotis Stefanides

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Date

Thursday 4 July 2019 8:11am

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