Method for drawing an antiprism with equilateral sides

honoluludesktop

???????????

jeff hammond

here's another solution that allows rotating without the mega-segment arc..

jeff hammond

PS :How many triangles must have the polyedra?
On the first post there are 8 on "the plan"
On the Xray Tig volume there are 7 !

i don't think it matters.. here's an example using octagons with one of them rotated 22.5 degrees then using the same exact method i used for the squares.. resulting in 16 equal sides. (i think the people trying it though are using the wiki example which has 7 sides.)

edit -- lol. the wiki one, the one i drew, the one tig drew..etc have 8 sides hah

TIG

@unknownuser said:

PS :How many triangles must have the polyhedron?
On the first post there are 8 on "the plan"
On the Xray TIG volume there are 7 !

@unknownuser said:

Won't the file lose some of its v7, and v8 features. Did v6 have "dynamic components", etc.?

there are rarely dynamic component in "hard geometry" like in this post or exotic functions

In my Xray volume there are 8 triangles BUT the left-hand-most one is almost square to the camera
A very neat solution by Jeff BTW...

TIG

If you think about it... as you increase the number of sides for the top and bottom faces the nearer they approximate the circles and the smaller the sides of the equilateral triangles forming the side facets so the 'height' decreases until with thousands of sides the top and bottom are approaching coplanarity...
The simplest form has equilateral triangular faces, the next squares and so on.
there are always twice as many sides as the edges to the faces: so the triangle solution has 3x2=6 sides, the square 4x2=8 sides and so on...

pilou

Ahhhh! I was victim of the perspective's law

pilou

Thx to Jeff for the "SU6 work"
(you use unity of the old 20 century
And Chris Fullmer for his Component onto face
Now I can see all 8 triangles!
The TIG's View was not good oriented!

TIG

To simplify things I have made a 'quick' Plugin - it's here http://forums.sketchucation.com/viewtopic.php?p=287140#p287140
You just type into the Ruby Console:
antiprism 7,1200.mm
and it'll makes a 7 sided antiprism with sides 1200mm long, centered on the origin and grouped, named 'Antiprism[7x1200]'...
You have to have at least 3 sides and a side-length > 0; the length is taken as inches if you haven't given a units suffix like 1.m or 100.cm or 1000.mm etc.
The distance between faces changes with the number of sides as the maximum 'rake' on the side-triangle occurs at with 3 sides, and it proportionately decreases as the number of sides increases, until you approximate to a circle with a multi-sided polygon, and by then the side-triangles are almost vertical...

pilou

Else a very speedy method

Draw Square A 1m * 1m (on the plan)
Copy rotate Square A 45° = Square B (on the plan)
Move Up Square B 1m on Z
Draw the 8 segments between 8 vertices
Select these 8 segments (method as you want)
Scale on Z (Blue Scale oposite point) 0.840892091m (magical number)
Move down Square B vertical snaped a triangle vertice
That's all

And then you can resize at any size for any cubic antiprism with the Tape Mesure tool
And all that without plugin, that is a real performance for me

sketchup_roolz

@tig said:

To simplify things I have made a 'quick' Plugin - it's here http://forums.sketchucation.com/viewtopic.php?p=287140#p287140

honoluludesktop

@unknownuser said:

Else a very speedy method .............And all that without plugin, that is a real performance for me :lol:
Genius:-)

jeff hammond

@unknownuser said:

Else a very speedy method

Scale on Z (Blue Scale oposite point) 0.840892091m (magical number)

frenchy, i think the challenge is to figure out a way to do it using only geometry/tricks available in sketchup. (ie- doing this in rhino for instance would be very easy)

that said, i think my method exposes a tolerance error in sketchup.. it shouldn't work but it does..

[edit, nevermind.. i just tried it with engineering/feet/.000001 precision and it does infact show the error..]

i couldn't figure out why i wasn't getting a ~ in front of my measurements because in my head, it should of been there..
-reason why there's an error: once you copy move the line up, make it perp to the hypotenuse, then rotate it /snap to the vert line, it doesn't end up being horizontal.. it's ever so slightly angled down.. i knew it was doing it but thought SU was thinking 'meh, close enough'..

but, after doing this exercise, i realize sketchup actually will say 'meh, close enough' when it comes to adding a ~ in front of certain measurements..

[edit]
the method i showed will give an equilateral triangle on one side but you'll see that it ever so slightly shifts the top square off center..

Jean Lemire

Hi Jeff, hi folks.

I noticed very small errors in the sides of the equilateral triangles. They are not all absolutely equal to 10 feet.

See you file with added dimensions.

antiprism_V6.skp

jeff hammond

hi Jean.
yeah, that's what i was talking about in the post just before yours.
i found the error too (and at first thought it was ok because sketchup wasn't giving me an approximate ~ measurement)

i came up with a way to do it in su only with no calculator but it's a bit drawn out and confusing.. i'll try another method when i get more time. (different than the hyper-segmented arc that tig showed -- which is probably the fastest/easiest)

but, i'm thinking you could come up with a clever method to accomplish it

pilou

@Jean
That is writed v6 but it is in fact v8 so the suspense is total for me

@Jeff
Maybe you must multiply scale by 10 000 then make the rotation for win some decimal?