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Questions tagged [polyhedra]

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2
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0answers
126 views

How can I get Mathematica 11 logo? [duplicate]

I want to get the picture(it is better to get the equations) of the mathematica 11 logo, how can I achieve that? I have try alpha to solve this, sadly, it only give me mathematica 1 logo. I want to ...
1
vote
1answer
103 views

Drawing polytope

Consider the $10 \times 3$ matrix ${\bf A}$ and the inequalities ${\bf A}{\bf x} \leq {\bf b}$: $$ \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 &1 \\ 1 & 0 & 0\\ 0 & 1 & 0\\ ...
8
votes
1answer
211 views

Constructing Icosahedral Fullerene Graphs

I am interested in constructing graphs of icosahedral fullerenes, following the construction explained in the first few pages of this article (alternate link). Mathematica has built-in information ...
1
vote
0answers
60 views

Polyhedra disappear in stl export [closed]

I've created a Graphics3D object from Polyhedra and Cylinders to display a graph in the following way: ...
1
vote
0answers
91 views

Intersection of two convex polyhedra with different set of faces

I want to solve the same question as the one in Difference (or intersection) of two convex polyhedra however my two convex polyhedra have two different set of faces f1 and f2, for example, not only ...
5
votes
1answer
143 views

What has changed in PolyhedronData in V11

As we saw in: Demonstration site CDF error correction question PolyhedronData has changed. I've failed to find any information about how the syntax changed in V11....
3
votes
0answers
331 views

How can I draw this phase diagram in Mathematica? [closed]

Currently, Master's student in Mathematical physics and I am doing research about QUANTUM CRyptography. Please can someone show me how to draw the phase diagrams for this function here? How can I ...
1
vote
0answers
60 views

Weird lines in my polyhedron [duplicate]

I'm seeing some weird artifacts on the corners of my Polyhedron: PolyhedronData["RhombicHexecontahedron"] Zooming in they look like this: Is this a bug?
2
votes
2answers
133 views

Geodesate vertices extraction

I'm not sure if this function is deprecated, but for some reason I find very little information about it. I use Geodesate to create an icosahedral grid: ...
9
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4answers
1k views

How to construct a 3D 10-sided Die (Pentagonal trapezohedron) and Spin to a face?

The Creating 3D dice question has answers for constructing a 6-sided die with images faces. I need to construct a 10-sided die with numbered faces. My first thought was to find 10-side polyhedra ...
3
votes
1answer
131 views

Technique for drawing polyhedron cutaway

Here is a graphic I drew with an earlier version of Mathematic (probably version 6) which I no longer have available: At the time Polyhedra was an external package,...
0
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1answer
182 views

Scale size PolyhedronData

How can I plot a truncated cube with size (sqrt(2)-1)? The code I am using is simply PolyhedronData["TruncatedCube"]
0
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0answers
123 views

Calling Polymake functions from Mathematica

I'm trying to do some polyhedral manipulations in Mathematica by using some functions from Polymake. But I have difficulty in passing the result from Mathematica to Polymake as an input without ...
-2
votes
1answer
148 views

How to get the actual Wolfram Language code to draw polyhedra in PolyhedronData?

PolyhedronData[] gives a nice collection of polyhedra. And calling PolyhedronData["DodecahedronIcosahedronCompound", "Image"] ...
19
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0answers
491 views

How to automatically pack irregular polyhedra [closed]

We get the tetrakaidecahedron like this: ...
31
votes
4answers
1k views

Faces and NetFaces relation in polyhedron

I'm trying to generate some plots of polyhedra with coloured faces. To determine the colours, I require the adjacency information of the faces. For the 3D plot this works really well. Say I want to ...
4
votes
1answer
676 views

How can I draw this polyhedron?

I'm high school student, and I am doing research about buildings using Mathematica. I want to plot the polyhedron shown below: I have tried using Table, but it ...
3
votes
1answer
262 views

ToElementMesh fails on DodecahedronIcosahedronCompound

Context I would like to compute the eigenmodes of a DodecahedronIcosahedronCompound. Why? Because it is cool! and I wonder how it rings… Starting with: ...
8
votes
6answers
1k views

How to draw a dodecahedron with each face modified to a pentagram?

I'd like to draw a dodecahedron with each face carved on the sides so it becomes a pentagram. I wonder how to start to do this kind of task in the Wolfram Language? Edit: The result should still be ...
45
votes
1answer
826 views

Random polyhedra walk

I would like to recreate ssch's random polyhedra random walk, which he posted in the chat. For convenience here it is again: This is my best attempt so far: You can download the notebook with the ...
0
votes
1answer
895 views

Drawing an dodecahedron with vertexes at given coordinates

I want to draw an (edit)dodecahedron with the vertex in the following coordinates: ...
5
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2answers
499 views

How do I show only the intrinsic color of 3D polygons?

System: Mathematica 9, Windows 7. I want to assign a polygon a color in such a way that it is rendered in that color irrespective of any ambient light sources. In other words I want Yellow to be ...
5
votes
1answer
517 views

Regular Polyhedra coordinate points generation

Is it possible to get all points on a Polyhedron surface using two surface parameters, say $ \phi,\theta $ spherical co-ordinates? Just like in ParametricPlot3D, ...
4
votes
2answers
308 views

How to make an octahedron 3-compound with holes?

I would like to remove facets from an octahedron 3-compound - like in the picture below. I tried to combine these two graphics: ...
5
votes
1answer
299 views

How can we get this infinite prism lattice to look more like `PolyhedronData[{“Prism”, 3}]`?

This is D$_3$h prism with order 12 (8 currently, needs 4 more edges) and rotational symmetry D$_3$ with order 6. A d=11 version is shown here. Using this code: ...
4
votes
2answers
454 views

Constructing a list of Cartesian coordinates of the Icosahedron

I’m learning Mathematica and I need the coordinates of the Icosahedron vertices. This is my attempt at writing a program for it. The vertex coordinates are simply all cyclic permutations and sign-...
6
votes
2answers
347 views

Simplify 2D polyhedral Regions like Interval

I don't think there's a built in "RegionSimplify" for polyhedral Regions and derived akin to how Interval automatically simplifies its argument expression: ...
1
vote
1answer
124 views

Plotting polyhedra faces with polygons removed from the interiors of the faces

I have dozens of vertices and dozens of faces which is why I use the v={};i={} and Graphics3D and ...
9
votes
2answers
664 views

Any packages for vertex enumeration on Mathematica?

My work requires me to enumerate all vertices of a polytope defined by linear inequalities from time to time. And I'm mainly working with _Mathematica 9.0 on Mac OS X 10.9. So I wonder are there any ...
10
votes
3answers
936 views

Torus triangulation

I'd like to plot something similar to this but with a triangle instead of a pentagon. Also, I'd like to triangulate the faces, that is, to insert the diagonals for each face of the 3 prisms used. In ...
3
votes
3answers
527 views

What is the order of faces on a D20? How can I optimize the order of faces on a D-n?

I am creating a customizable D20 for 3D printing using OpenSCAD, with the following code: ...
6
votes
1answer
725 views

How to construct a polyhedron from its vertex graph?

Consider the graph given by ...
21
votes
2answers
2k views

Difference (or intersection) of two convex polyhedra

I have two convex polyhedra stored in the following form: a set of vertices vertices = {{x1,y1,z1},...}, a set of faces, where each face is a convex polygon ...
3
votes
1answer
122 views

Symbolic Output after numerical computation

I have a small question about the symbolic output. I started to write a program that generates the coordinates of n-dimensional polytopes by Wythoff construction. For crystallographic groups, all is ...
2
votes
2answers
457 views

Plotting a Spericon and Bipyramid with 100 faces

I would like to plot convex polyhedron with 100 faces, which could be used as a die. My first attempt was asking for Conway's Hecatohedron. Unfortunatly, it can not be used as a die. Now there are ...
2
votes
1answer
337 views

Plotting John Conway's Hecatohedron

John Conway has given an explanation how a regular Hecatohedron (polyhedron with 100 faces) looks like: http://www.ics.uci.edu/~eppstein/junkyard/hecatohedron.html Conway explains: Here's a ...
0
votes
1answer
200 views

How to plot a decahedron with Mathematica?

I wrote Graphics3D[{Opacity[.9], FaceForm[Yellow], PolyhedronData["Dipyramid", "Faces"]}] and I get this picture: I would like to plot a decahedron without any ...
1
vote
0answers
228 views

How to mathematically represent MMA 9 Spikey?

I am trying to figure out how to mathematically represent the MMA 9 Spikey in order to send to a 3D printer. According to this page, " In particular, spikeys for version 2 and up are based on a ...
7
votes
6answers
1k views

How to find the vertices of a regular tetrahedron? a dodecahedron?

My question is: how to find the coordinates of the vertices of regular tetrahedron and dodecahedron? I tried to find the coordinates of the vertices of a regular tetrahedron as the solutions of a ...
7
votes
2answers
1k views

Draw an arbitrary convex polyhedron without excess diagonals drawn

I want to draw a set of convex polyhedrons whose vertices are defined by spherical coordinates on the surface of a unit sphere. Currently I followed the advice from here: https://mathematica....
0
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0answers
65 views

Draw an arbitrary convex polyhedron [duplicate]

I want to draw a set of convex polyhedrons whose vertices are defined by spherical coordinates on the surface of a unit sphere. How can I accomplish this in Mathematica? It seems I cannot do it ...
2
votes
1answer
679 views

Finding 111 plane of Carbon Diamond

All, I looked at the example on the Mathematica Website with the Carbon Diamond Lattice. Example I am referring to I am wondering is there a way to highlight an individual plane such as the 111 or ...
22
votes
5answers
3k views

Insphere for Irregular Tetrahedron

I am looking for existing Mathematica code to compute the unique sphere inscribed inside an irregular tetrahedron. I can write it myself, but I would love to find that someone already performed this ...
2
votes
1answer
305 views

Viewing the inside of cuboid intersections

    I have a number of cuboids intersecting as illustrated. I would like to see their intersection, almost the view from inside. Setting the ...
18
votes
3answers
3k views

Checking if a point is in a convex 3D polyhedron

Extending from these questions How to check if a 3D point is in a planar polygon? and How to check if a 2D point is in a polygon?. I'm trying to do this to render specific shapes made up of spheres. ...
24
votes
2answers
3k views

Generating convex polyhedron from face planes?

Suppose I have lists of normals and points for planes. There's a convex polyhedron whose faces lie on these planes and are bounded by plane intersections. What would be the easiest way to produce an ...