Πεντάγραμη Ψευδόγεωδαιτική Σφαίρα - Pentagram Pseudogeodesic sphere

Έδρες: 92 (60 ισόπλευρα τρίγωνα, 20 κανονικά εξάγωνα, 12 κανονικά πεντάγωνα)

Ακμές: 180

Κορυφές: 92

Faces: 92 (60 equilateral triangles, 20 regular hexagons, 12 regular pentagons)

Edges: 180

Vertices: 92

Geomag Elements:

Spheres: 110

Rods: 300 (180 Blue, 120 Silver)

Triangles: 60

Pentagons: 12

Bασισμένο στο έργο των (based on the work of)

Rafael Millán

http://textodigital.com/P/GG/bgeod1.php

Wolfram Research Inc.

http://mathworld.wolfram.com/SmallDodec ... edron.html

The truth is that I was trying to build the uniform polyhedron U62 small dodecahemicosahedron using pentagons, triangles and rhombus (3 for the hexagons, despair!!!) and hoping some how (?) to look like the model of Wolfram http://mathworld.wolfram.com/SmallDodec ... edron.html

Bad idea!!!

Then I change the plan and I try to build the uniform polyhedron U36 dodecadodecahedron using 3 squares in right angles among them for the hexagons between the pentagrams http://mathworld.wolfram.com/Dodecadodecahedron.html

But the opening among the triangles of the pentagrams is bigger than the edges of the hexagons!!!

Another bad idea!!!

I was standing hopeless feeling like an idiot, when I remember that the first shape I build seem familiar.

So when something in geomag feels like you saw it before the only thing you can do is to go to the maestro page and to find what you have re-invented.

The maestro has build! It !!

It was the Pseudogeodesic sphere or a variation of it!!!

Again the maestro beat me in the end!!!

Αστεροειδές Εικοσιδωδεκάεδρο - Stellated Icosidodecahedron

The stellated icosidodecahedron is a dodecahedron intersected with a icosahedron.

The dodecahedron and the icosahedron are duals.

Dodecahedron: 12 faces, 20 vertices, 30 edges

Icosahedron: 20 faces, 12 vertices, 30 edges

They also share the same polyhedra when they are truncated.

The term "stellated" means that this polyhedron can be created by extending the faces of the icosidodecahedron.

Geomag Elements:

Spheres: 74 (62 1/2 ’’ in (12.7 mm) + 12 1’’ in (25.4 mm))

Rods: 300 (120+180)

Bασισμένο στο έργο των (based on the work of)

Lazaros Motsanos (My first original yeah!!!)

And

Coolmath4kids.com

http://www.coolmath4kids.com/polyhedra/ ... edron.html

The making of stellated icosidodecahedron is very easy, first you build a Icosidodecahedron (I use the silver rods), then you put in every triangle of the Icosidodecahedron three rods and one sphere (the shape is now a Rhombic Hexecontahedron) and for the end you use ten rods and one sphere (I used a 1” sphere because there isn’t a lot of space for the rods-thank for the idea Karl!!-) in every pentagon of the Icosidodecahedron, and finish.

The inspiration for this was the work of two great master of the geomag art Karl Horton (Small stellated dodecahedron) and Peter Jepsen (Great stellated dodecahedron).

That three (Rafael Millán, Karl Horton, Peter Jepsen) is the reason I’m in love with the geomag art.

Thank you for my new love guys !!!