Platonic relationships

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Platonic relationships

What is the dihedral angle of the icosahedron? The dihedral angle is the angle formed by the intersection of 2 planes: See Figure 4 as well. Figure 10 If we lay a 3D model of the icosahedron on one of its sides, we can see that a line through the centroid O is perpendicular to that side.

So the triangle OXB, for example, is right. Now lets get to the interesting stuff! Going back to figure Platonic relationships, we can see that the icosahedron is composed of interlocking pentagonal 'caps.

Platonic relationships

D is directly over the point Q in the icosahedron. In other words, what is the distance DQ? QF is the radius of that circle. Therefore we write Hmmm, this is looking interesting. Lets compare FQ to DQ.

How do all of these distances relate to the diameter of the enclosing sphere, DI?

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In fact, if you place 3 of these rectangles perpendicular to each other, the 12 corners of the 3 rectangles are the vertices of the icosahedron! Figure 7, repeated I have copied Figure 7 from above. One interesting fact appears here: This means that the distance from one pentagonal plane to the other is precisely the radius of the circle that encloses the pentagon!

All of these relationships come from the pentagon! On the outside of the icosahedron, we see equilateral triangles.

But the guts of this polyhedron comes from pentagonal relationships.

Platonic relationships

The equilateral triangles come about from the lifting of the pentagonal 'cap' vertex off the pentagonal plane. There is now no question that the basis for the construction of the icosahedron is the pentagon.

Take a look at this view of the icosahedron: Figure 15 As you can see, the 2 pentagonal planes in the middle have magically disappeared and become equilateral triangles! It seems that all of our work is wrong, except: The equilateral triangle faces of the icosahedron are a by-product of how the pentagons interlock.Krista J.'s husband is hanging out with another that wrong?

"He told me they are just friends, but he has been leaving me to go hang out with her," she frets. As readers offer Krista. Dec 21,  · A relationship can never be truly platonic if you have to adjust your feelings.

A relationship can never truly be platonic if you have to pretend that you are happy with the way things really are. The Bible and homosexuality Same-sex relationships in the Bible.

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The Bible and homosexuality

We will attempt to give interpretations of key passages of the Bible from both a conservative (fundamentalist and other evangelical) and from a liberal position. Build healthy relationships and learn to show more affection with the help of wikiHow's Relationships category.

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Whether you want to be an expert at cuddling or just want to know when someone likes you romantically, we've got advice for you! In most cases, this is a Sub-Trope of Like Brother and difference is that for Platonic Life Partners, their relationship with each other is the most important relationship, with even romantic relationships coming in second.

Rent A Gent is a startup that lets you rent a platonic male friend for $ an hour — here's what it's like to use.

Platonic Relationships — Everything you wanted to know but didn't know who to ask!