Favourite Platonic Solid

Michael Wallace · Post by **Michael Wallace** » Sat Aug 29, 2009 12:51 pm

Or, another excuse to talk about cubes.

Jon O'Neill · Post by **Jon O'Neill** » Sat Aug 29, 2009 1:14 pm

Octahedra are butters lol

Sue Sanders · Post by **Sue Sanders** » Sat Aug 29, 2009 1:14 pm

Michael Wallace wrote:Or, another excuse to talk about cubes.

I like Octagonals (I design many a garden with an octagonal patio) so I voted for an Octo-thingy

I don't want to talk about cubes though. And I'm a bit all dried out on the Religion poll at the moment.

I'm going to talk swedes with Ian Volante.

Byeeeeee

Matt Morrison · Post by **Matt Morrison** » Sat Aug 29, 2009 4:09 pm

Right now, Octahedron.

Sue Sanders · Post by **Sue Sanders** » Sat Aug 29, 2009 4:13 pm

Ian and I have exhausted swedes so I've returned and also voted for Raccoon. I might start introducing secret raccoons into my garden designs.

Dinos Sfyris · Post by **Dinos Sfyris** » Sat Aug 29, 2009 4:22 pm

Bucky Ball for me

Peter Mabey · Post by **Peter Mabey** » Sat Aug 29, 2009 5:55 pm

http://en.wikipedia.org/wiki/File:Great ... hedron.png

Rosemary Roberts · Post by **Rosemary Roberts** » Mon Aug 31, 2009 10:32 am

Peter Mabey wrote:http://en.wikipedia.org/wiki/File:Great ... hedron.png

You're a fan of interpenetration?

I prefer the spiky one http://en.wikipedia.org/wiki/File:Small ... hedron.png. Used to have one on my desk.

Matt Morrison · Post by **Matt Morrison** » Mon Aug 31, 2009 8:01 pm

Peter Mabey · Post by **Peter Mabey** » Mon Aug 31, 2009 9:27 pm

Rosemary Roberts wrote:
Peter Mabey wrote:http://en.wikipedia.org/wiki/File:Great ... hedron.png
You're a fan of interpenetration?

My favourite for interpenetration is http://en.wikipedia.org/wiki/File:Compo ... ahedra.png
I have made a model, but it's now lost.

Michael Wallace · Post by **Michael Wallace** » Mon Aug 31, 2009 9:29 pm

Just a quick note to say I've set this poll to finish on Saturday, so that we'll have a definitive answer.

Rosemary Roberts · Post by **Rosemary Roberts** » Mon Aug 31, 2009 10:05 pm

Peter Mabey wrote:
Rosemary Roberts wrote:
Peter Mabey wrote:http://en.wikipedia.org/wiki/File:Great ... hedron.png
You're a fan of interpenetration?
My favourite for interpenetration is http://en.wikipedia.org/wiki/File:Compo ... ahedra.png
I have made a model, but it's now lost.

Agreed! I had one of those as well but it got crushed in a move. All that survives of our collection was a very boring series of successively trucated tetrahedra. I will have to persuade him-that-does-the precision-engineering to make another 5-tetrahedra.

Charlie Reams · Post by **Charlie Reams** » Wed Sep 02, 2009 4:35 pm

I saw a nice STEP question once that basically asked you to prove that there were exactly five Platonic solids. And now, 5 years later, I can't remember how to do it at all.

JackHurst · Post by **JackHurst** » Wed Sep 02, 2009 4:52 pm

Charlie Reams wrote:I saw a nice STEP question once that basically asked you to prove that there were exactly five Platonic solids. And now, 5 years later, I can't remember how to do it at all.

I had a lecture on it at Leeds.
I can recall some of it, heres a shabby explanation.

Its do do with how the internal angles of the shape you are using for the faces can add up to less then 360

Each face must be a regular polygon, and all the faces must be the same.
You must have at least 3 faces meeting at a vertex to form a polyhedron
So at each vertex thee corners of the faces that meet must add up to less then 360 degrees.

For triangular faces you can have 3, 4, or 5 meeting at a vertex
For square faces you can only have 3 meeting at a vertex
For pentagonal faces you can only have 3 meeting at a vertex
For Hexagonal you can have 3 meeting
For heptagonal you can't have 3 because the internal angles of 7 heptagon vertices is more then 360.

3 triangles at a vertex is a tetrahedron, i think 4 triangles at a vertex is the octahedron, 3 squares at one vertex is the cube, 3 pentagons at each vertex is the dodecahedron, and 5 triangles at each is the icosahedron. (Dunno if i've matched these bits up right, i was just getting)

How did you do when you sat the step Charlie?

Charlie Reams · Post by **Charlie Reams** » Wed Sep 02, 2009 5:07 pm

JackHurst wrote:How did you do when you sat the step Charlie?

Let's just say my grades were good enough to get into the Unseen University.

Clive Brooker · Post by **Clive Brooker** » Wed Sep 02, 2009 5:32 pm

JackHurst wrote:
Charlie Reams wrote:I saw a nice STEP question once that basically asked you to prove that there were exactly five Platonic solids. And now, 5 years later, I can't remember how to do it at all.
I had a lecture on it at Leeds.
I can recall some of it, heres a shabby explanation.

Its do do with how the internal angles of the shape you are using for the faces can add up to less then 360

Each face must be a regular polygon, and all the faces must be the same.
You must have at least 3 faces meeting at a vertex to form a polyhedron
So at each vertex thee corners of the faces that meet must add up to less then 360 degrees.

For triangular faces you can have 3, 4, or 5 meeting at a vertex
For square faces you can only have 3 meeting at a vertex
For pentagonal faces you can only have 3 meeting at a vertex
For Hexagonal you can have 3 meeting
For heptagonal you can't have 3 because the internal angles of 7 heptagon vertices is more then 360.

3 triangles at a vertex is a tetrahedron, i think 4 triangles at a vertex is the octahedron, 3 squares at one vertex is the cube, 3 pentagons at each vertex is the dodecahedron, and 5 triangles at each is the icosahedron.

I think this proves that there are no more than 5, but doesn't establish that all five possibilities lead to a regular polygon. But university was a long time ago.

Rosemary Roberts · Post by **Rosemary Roberts** » Wed Sep 02, 2009 9:08 pm

JackHurst wrote:How did you do when you sat the step Charlie?

Is this something to do with the naughty step we hear so much about? Are toddlers supposed to study solid geometry now?

Phil Reynolds · Post by **Phil Reynolds** » Wed Sep 02, 2009 9:19 pm

Rosemary Roberts wrote:Are toddlers supposed to study solid geometry now?

I gather from breeding friends of mine that a toddler's first manufacture of solids is regarded as some kind of cause for celebration.

Rosemary Roberts · Post by **Rosemary Roberts** » Wed Sep 02, 2009 9:27 pm

Phil Reynolds wrote:
Rosemary Roberts wrote:Are toddlers supposed to study solid geometry now?
I gather from breeding friends of mine that a toddler's first manufacture of solids is regarded as some kind of cause for celebration.

True, but geometric figures didn't use to be a requirement. Is this the next Olympic sport?

(Well done Phil, managing to get your friends to breed! Most of ours have remained stubbornly uncooperative.)

Kevin Thurlow · Post by **Kevin Thurlow** » Thu Sep 03, 2009 7:06 am

Dinos said "Bucky Ball for me "

Yes - me too! Just try naming it though.....

Matt Bayfield · Post by **Matt Bayfield** » Thu Sep 03, 2009 7:38 am

Not being a mathematician (or knowledgeable type) I didn't know what "platonic solid" meant until reading this thread. Now I do... I feel educated.

Phil's mention of baby solids reminds me of a Hale & Pace sketch from the early 90s, where an unbelievably precious and pretentious couple, who are new parents, are at a dinner party. They change every topic of conversation to their precious new baby Joshua, oblivious that everyone else finds the minutae of little Joshy's routine utterly tiresome and uninteresting. The punchline occurs when they receive dessert - a chocolate mousse - and gush "ooh look - it's just the same colour as little Joshy's faeces"...

...and what's worse, people like this do exist. I have had to suffer at least one conversation with friends about their new offspring's excreta.

And don't get me started on people who have "baby on board" signs in the back of their vehicles.

Kai Laddiman · Post by **Kai Laddiman** » Thu Sep 03, 2009 8:02 am

Phil Reynolds wrote:I gather from breeding friends of mine

You breed your own friends?

Jon Corby · Post by **Jon Corby** » Thu Sep 03, 2009 8:19 am

Matt Bayfield, what do you think of people who have "Baby On Board" signs in their car?

Phil Reynolds · Post by **Phil Reynolds** » Thu Sep 03, 2009 9:15 am

Rosemary Roberts wrote:Well done Phil, managing to get your friends to breed!

I'm afraid those that are so inclined do so without encouragement from me. In fact, I try to persuade them not to as it means we probably won't see them socially for another 15 years or so.

Phil Reynolds · Post by **Phil Reynolds** » Thu Sep 03, 2009 9:16 am

Kai Laddiman wrote:You breed your own friends?

No, I find it's easier to adopt other people's.

Matt Bayfield · Post by **Matt Bayfield** » Thu Sep 03, 2009 9:17 am

Bait accepted, Jon. The following rant to be taken with a pinch of salt. I'm sure it will at least mildly offend someone so I'll make my apology for the offence, but not my opinion, in advance.

[off-topic rant]

Utterly ridiculous things, "baby on board"/"child on board" signs. Ostensibly marketed as a safety feature (i.e. if we have an accident, please look for a child in the wreckage - as if the emergency services wouldn't do so anyway!), but in reality marketed to, and displayed by, parents who wish to give the message "aren't we wonderful, because we have made a baby". As if that, in itself, is something remarkable and unusual. Seriously, fellow parents, be justifiably proud when you've raised a child to be of good character and a valued member of society, but regardless of any biological misfortune you may have, don't expect me to give you any credit before then just for having knocked one out, okay?

And in case anyone's not convinced, the marketing as a safety feature is definitely a sham, because I don't know anyone who takes the sign out when travelling without their children.

As you can probably guess, I don't have a "child on board" sign in my car.

[/off-topic rant]

Phil Reynolds · Post by **Phil Reynolds** » Thu Sep 03, 2009 9:23 am

Matt Bayfield wrote:Utterly ridiculous things, "baby on board"/"child on board" signs.

True, but without them we'd never have had the Be Sharps' greatest hit.

Rosemary Roberts · Post by **Rosemary Roberts** » Thu Sep 03, 2009 10:46 am

Matt Bayfield wrote:Utterly ridiculous things, "baby on board"/"child on board" signs.

I always understood them to mean "if you are going to crash into another car, please do not choose this one." Which is not likely to be very effective - given that it is addressed to people who are not looking where they are going.

The emergency services are likely to be guided by the presence of a child seat. And if the child is lucky, by the loud screams.

Sue Sanders · Post by **Sue Sanders** » Thu Sep 03, 2009 11:07 am

Matt Bayfield wrote: Utterly ridiculous things, "baby on board"/"child on board" signs.

Don't forget the equally irritating ' "Mum-to-be" on board'

don't expect me to give you any credit before then just for having knocked one out, okay?

Totally unconnected, but I'm reminded that in last night's Eggheads', Dermot advised the challengers that they had the opportunity to 'knock one more out in the final round' .

Charlie Reams · Post by **Charlie Reams** » Thu Sep 03, 2009 11:09 am

Sue Sanders wrote:Dermot advised the challengers that they had the opportunity to 'knock one more out in the final round' .

I guess that's one way to beat off the opposition.

Ian Volante · Post by **Ian Volante** » Fri Sep 04, 2009 7:10 am

Charlie Reams wrote:
Sue Sanders wrote:Dermot advised the challengers that they had the opportunity to 'knock one more out in the final round' .
I guess that's one way to beat off the opposition.

Chris Hughes has a shiny enough head already.

Matt Morrison · Post by **Matt Morrison** » Sat Oct 03, 2009 12:58 am

Kubrick's Rube

Phil Reynolds · Post by **Phil Reynolds** » Sat Oct 03, 2009 9:41 am

Matt Morrison wrote:Kubrick's Rube

That is very, very good indeed. I like the fact that you can solve it in two ways: all squares on each face the same colour, or all squares on each face the same film.

Edit: actually, maybe you can't. I've identified six films from the visible squares, but there are some images I don't recognise, so unless they're from one of the films I've already spotted, there are more than six.

Michael Wallace · Post by **Michael Wallace** » Sat Oct 03, 2009 2:00 pm

I see the poll's finished. Icosahedron is disqualified for...something or other.

Matt Morrison · Post by **Matt Morrison** » Sat Feb 19, 2011 12:19 pm

Joseph Krol · Post by **Joseph Krol** » Sat Feb 19, 2011 12:27 pm

Go Icosahedrons! The thing which has the most twentysidedness that I know of.

Soph K · Post by **Soph K** » Sat Feb 19, 2011 6:32 pm

i like dodecahedrons best cos once in maths my teacher said what are dodecahedrons (and we'd never heard of em before) and someone in my class said its a type of sauce isnt it like brown sauce (lol) so teacher obv laughed and said no this is a maths lesson and another person said is it a 3D 12 sided shape and teacher said yeah well done and my friend was gonna say that too so she went DOH DOH DOH and then everyone just started saying DOH!-DECAHEDRON DOH!-DECAHEDRON (the teacher was luckily outside classroom answering phone and we werent doing the DOH!-DECAHEDRON thing too loud so she didnt notice we were doing it) and it was so funny and i was just sitting there staring at everyone like what on earth...!

Thomas Carey · Post by **Thomas Carey** » Tue Feb 22, 2011 11:45 am

I'll say dodecahedrons because tetrahedrons and icosahedrons have the most/least sides so they don't count, cubes are way too common and octahedrons have no purpose.

Soph K · Post by **Soph K** » Tue Feb 22, 2011 11:50 am

GO DODECAHEDRONS!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Rosemary Roberts · Post by **Rosemary Roberts** » Tue Feb 22, 2011 12:20 pm

Thomas Carey wrote:octahedrons have no purpose.

Not so! How would you make one of these

without them?

Thomas Carey · Post by **Thomas Carey** » Tue Feb 22, 2011 6:33 pm

Rosemary Roberts wrote:
Thomas Carey wrote:octahedrons have no purpose.
Not so! How would you make one of these without them?

Stick a load of square based pyramids together.

Joseph Krol · Post by **Joseph Krol** » Tue Feb 22, 2011 6:36 pm

Thomas Carey wrote:
Rosemary Roberts wrote:
Thomas Carey wrote:octahedrons have no purpose.
Not so! How would you make one of these without them?
Stick a load of square based pyramids together.

Haha good answer.

Rosemary Roberts · Post by **Rosemary Roberts** » Tue Feb 22, 2011 6:49 pm

Thomas Carey wrote:Stick a load of square based pyramids together.

That might qualify as an engineering solution, but hardly a mathematical model.

Favourite platonic solid?