### Hexagons

Shared publicly -In this tutorial, you'll learn how to create hexagon grids for all sort of sci-fi stuff or material treatments using the Hexagon Grid Creator script in Maya.

1

Add a comment...

AboutPostsPhotosVideos

In this tutorial, you'll learn how to create hexagon grids for all sort of sci-fi stuff or material treatments using the Hexagon Grid Creator script in Maya.

1

Add a comment...

Due to come onto the market in summer next year, Hexi-House is a hexagonal pod building system which will be of interest to shedworkers, aimed squarely at the garden buildings market and specifically at those keen to invest in garden offices. The pods come ...

2

Add a comment...

Dots that are moving around in a circle! Connect them and you'll get a moving octahedron!

#octahedron

#octahedron

7

4

Add a comment...

Over 15 Handpicked Hexagonal Social Media Icons http://buff.ly/1bYoymk

1

Add a comment...

I can't believe I'm creating a Google+ event for this again.

Yes it's almost Hexagonal Awareness Month. For details plz see:

http://hexagonalawarenessmonth.com/

That is all. Thank you.

Yes it's almost Hexagonal Awareness Month. For details plz see:

http://hexagonalawarenessmonth.com/

That is all. Thank you.

6

3

3 comments

Art Ibiza

+

1

2

1

2

1

Yeah!!! We are +6!!!!

Add a comment...

In their circles

160 people

This is the **{6,3,6} honeycomb**, as drawn by +Roice Nelson. It's also called the **order 6 hexagonal tiling honeycomb**. The reason is that has a lot of sheets of regular hexagons, and 6 sheets meet along each edge of the honeycomb.

I've already showed you honeycombs where 3, 4, or 5 sheets of hexagons meet along each edge. They all live in hyperbolic space, and you can see them all starting here:

http://blogs.ams.org/visualinsight/2014/05/01/636-honeycomb

But now we've reached the end! Like life itself, some patterns in math are finite - and all the more precious for that reason. You can do 6, but you can't build a honeycomb in hyperbolic space with 7 sheets of hexagons meeting at each edge.

**Puzzle:** what do you get if you try?

I don't know, but it's related to this:

• You can build a tetrahedron where 3 triangles meet at each corner. For this reason, the tetrahedron is also called {3,3}. You can build a hyperbolic honeycomb where the edges coming out of any vertex go out to the corners of a tetrahedron... and these edges form hexagons. This is the**{6,3,3} honeycomb**.

• You can build an octahedron where 4 triangles meet at each corner. The octahedron is called {3,4}. You can build a hyperbolic honeycomb where the edges coming out of any vertex go out to the corners of an octahedron... and these edges form hexagons. This is the**{6,3,4} honeycomb**.

• You can build an icosahedron where 5 triangles meet at each corner. The icosahedron is also called {3,5}. You can build a hyperbolic honeycomb where the edges coming out of any vertex go out to the corners of an icosahedron... and these edges form hexagons. This is the**{6,3,5} honeycomb**.

• You can build a tiling of a flat plane where 6 triangles meet at each corner. This triangular tiling is also called {3,6}. You can build a hyperbolic honeycomb where the edges coming out of any vertex go out to the corners of a triangular tiling... and these edges form hexagons. This is the**{6,3,6} honeycomb**.

The last one is a bit weird! The triangular tiling has*infinitely many* corners, so in the picture here, there are *infinitely many* edges coming out of each vertex. For other weird properties of the {6,3,6} honeycomb, read my blog article.

But what happens when we get to {6,3,7}?

#geometry

I've already showed you honeycombs where 3, 4, or 5 sheets of hexagons meet along each edge. They all live in hyperbolic space, and you can see them all starting here:

http://blogs.ams.org/visualinsight/2014/05/01/636-honeycomb

But now we've reached the end! Like life itself, some patterns in math are finite - and all the more precious for that reason. You can do 6, but you can't build a honeycomb in hyperbolic space with 7 sheets of hexagons meeting at each edge.

I don't know, but it's related to this:

• You can build a tetrahedron where 3 triangles meet at each corner. For this reason, the tetrahedron is also called {3,3}. You can build a hyperbolic honeycomb where the edges coming out of any vertex go out to the corners of a tetrahedron... and these edges form hexagons. This is the

• You can build an octahedron where 4 triangles meet at each corner. The octahedron is called {3,4}. You can build a hyperbolic honeycomb where the edges coming out of any vertex go out to the corners of an octahedron... and these edges form hexagons. This is the

• You can build an icosahedron where 5 triangles meet at each corner. The icosahedron is also called {3,5}. You can build a hyperbolic honeycomb where the edges coming out of any vertex go out to the corners of an icosahedron... and these edges form hexagons. This is the

• You can build a tiling of a flat plane where 6 triangles meet at each corner. This triangular tiling is also called {3,6}. You can build a hyperbolic honeycomb where the edges coming out of any vertex go out to the corners of a triangular tiling... and these edges form hexagons. This is the

The last one is a bit weird! The triangular tiling has

But what happens when we get to {6,3,7}?

#geometry

1

1

Add a comment...

This drawing by +Roice Nelson shows what you'd see if you lived in hyperbolic space and filled this space with a

Hyperbolic space is curved, but each hexagon here lies on a flat plane inside hyperbolic space. Each of these plane is tiled with hexagons in the usual way, 3 meeting at each corner.

However, each edge in this picture has 3 different planes like this going through it! Planes of hexagons, 3 hexagons meeting at a corner, with each edge lying on 3 planes - that's the reason for the symbol {6,3,3}.

For much more about this honeycomb and its relatives, visit my

http://blogs.ams.org/visualinsight/2014/03/15/633-honeycomb/

It contains a puzzle for true math fans:

#geometry

3

1

Add a comment...

Join the Interdependence Hexagon Project 2014.

Explore our interconnectedness visually and with text.

Open to youth ages 8 to 18 and all ages in the People's Hexagon Project. Deadline for Schools: June 30.

All materials can be found on our NEW website at www.hexagonproject.org

Explore our interconnectedness visually and with text.

Open to youth ages 8 to 18 and all ages in the People's Hexagon Project. Deadline for Schools: June 30.

All materials can be found on our NEW website at www.hexagonproject.org

1

Add a comment...

Here we see the illustrious cuboctahedron, or vector equilibrium. Along with the truncated octahedron, it can be considered, in some sense, a three-dimensional analogue to the hexagon. Though it has no hexagonal faces, the cuboctahedron can be seen to consist of four hexagonal rings or planes arranged in the manner of tetrahedral symmetry. That is, if one took a tetrahedron, replaced its four faces with hexagons (as for instance with a truncated tetrahedron), and collapsed all four hexagonal sides so that they all shared a common center, the vertices of the hexagons would describe a cuboctahedron, with each vertex shared between two intersecting hexagons, collapsing the original 24 vertices of the four hexagons into the 12 vertices of the cuboctahedron. (Likewise, of course, the cuboctahedron can simply be seen as a sort of "expanded" tetrahedron, with four of its eight triangular faces representing the original four faces of an inner tetrahedron, the remaining four triangles representing its four vertices, and the square faces representing its edges.) Tetrahedral symmetry being the simplest type of polyhedral symmetry, and the only one suited to this sort of fitting together of hexagonal planes, the cuboctahedron represents a unique extension of and analogue to hexagonal symmetry in three dimensions.

4

4

Add a comment...

Now if I just knew how to make a plexiglass hexagonal bubble about 25-27 feet in every direction.

1

Add a comment...

People

In their circles

160 people

Contact Information

Contact info

Phone | 978.800.1218 |

Story

Tagline

Hexagons are polytopes with six edges and six vertices.

Introduction

Hexagons are one of the most robust and versatile shapes available today. Regular hexagons and hexagonal symmetries can be found throughout the natural world, including in crystal structures, convection cells, arthropod nests, etc. Hexagons also play an important role in geometry, number theory, and other pertinent and interesting areas of mathematics. It is possible that the universe itself is a hexagon. It is likely that HEXAGONS will continue to increase in popularity over the coming years, as humanity enters a glorious new hexagonal golden age, and all sentient beings on our planet ascend to a new, higher state of hexagonal consciousness.

For discussion of hexagons and hexagon-related issues, please consider joining our sibling Google entity, the Hexagon-Group on Google Groups:

⬢ ⬡ ⬢ ⬡ ⬢ ⬡