# Questions tagged [polyhedra]

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### RegionDistance and SignedRegionDistance do not work with Polyhedron objects

I have reported this behaviour to WRI. A support case was created with the ID [CASE:4544288] Consider this simple example (tested in Mathematica 12.0 and 12.1): ...
107 views

### My first Mathematica project code review, Dodecahedron

I thought of a project to get my feet wet with Mathematica and have completed it. If anyone finds time to look at the code and send some feedback I would appreciate it. If it's inappropriate to ask ...
59 views

### Generating family of demicube graphs

I've been using the built-ins HypercubeGraph[n] and TuranGraph[2 n, n] to explore properties of the $1$-skeletons of the $n$-...
79 views

### Region function of rotated Polyhedron

Is it possible to find the equation of the internal region of a rotated polyhedron? For example, the analytic region for a Dodecahedron is found by: ...
41 views

### Display minimum distance and minimum-distance path between two points on a polyhedron

Given a genus-zero polyhedron (e.g., PolyhedronData["Dodecahedron"]) and a point $P$ anywhere on its surface, color all points on the polyhedron by the length of ...
48 views

### scale the size of analytic region obtained form PolyhedronData

I would like to know if it is possible to find the equation of the internal region of a polygon, whose size has been rescaled. For example: The analytic region for a Dodecahedron is founded of: <...
57 views

### Octahedra+tetrahedra filling tessellations in 3D

This is called the quasiregular space-filling tessellations in 3D: formed by Octahedra in RED and tetrahedra in YELLOW Are there any smart ways to do a Mathematica figure drawing this?
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### Draw a truncated octahedron packing in 3D

Consider a truncated octahedron composed by 24 vertices (4×6) 14 faces (contain 6 squares and 8 hexagons) 36 edges (4×6+6×82=36). This truncated octahedron can pack and tessellate the 3-dimensional-...
62 views

### How to export HyperbolicPolyhedron as STL?

Here's the starting point (It's the Mathematica "Spikey 2" logo): Graphics3D[HyperbolicPolyhedron["Dodecahedron", 1.3], Boxed -> False] Here is the link to ...
77 views

### Geodesate extract angles and edges length of a polyhedron

I'm using Mathematica 11, don't have access to new functions in Geodesate. Edited to clarify my question What I aim to do, it is to extract the angles and length of edges of a polyhedron (also in ...
260 views

### Color the polygons in PolyhedronData

What is the simplest method for coloring each polygon face of a polyhedron with a specified color? For instance suppose I have a list of $12$ colors (...
146 views

### Unfolding a polyhedron

I wanted to know how unfolding a Polyhedron in Mathematica works. I can't seem to make it work even when I have all the coordinates I need. The Polyhedron of reference is ...
90 views

### Changing the length of the edge of the Polyhedron

Hope you're having a great day! I made another post in regard of how to insert an image onto a face of a Polyhedron. I hope you could help me on this one too! I want to change the length of the ...
150 views

### Modify each version of the polyhedron with an image

I'm new here and want to represent a Polyhedron with every face filled with my own Image of choice. The Polyhedron is the DuerersSolid: ...
173 views

### Symmetrical rotating tetrahedron

How to find the vertices of a regular tetrahedron? a dodecahedron? I already get the coordinate of the tetrahedron, but i don't know how to rotate it just like the gif
400 views

### How can I obtain and work with a Platonic dodecahedron?

I want to obtain and work with a Platonic dodecahedron like this one: I don't have basic knowledge needed to do it. Can anyone can help me? Just the basics to get me started.
114 views

### Fill points into a pre-rotated convex Dodecahedron

I am trying to fill a rotated convex polyhedron with points. This functions well in the unrotated case: ...
125 views

### Creating a polyhedron filled with points in face-centered cubic structure

I am relatively new to Mathematica, and I am trying to build a 3D polyhedron model filled with points in a face-centered cubic (fcc) pattern that shall represent atoms. I am running on Mathematica 11....
90 views

### Rotate PolyhedronData

I'd like to create a Graphics3D rendering of a rotated Polyhedron taken from PolyhedronData[] ...
164 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 ...
216 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\\ ...
273 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 ...
94 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: ...
103 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 ...
169 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....
441 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 ...
67 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?
166 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: ...
2k 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 ...
229 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,...
257 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"]
160 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 ...
188 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"] ...
585 views

### How to automatically pack irregular polyhedra [closed]

We get the tetrakaidecahedron like this: ...
2k 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 ...
828 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 ...
308 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: ...
2k 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 ...
940 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 ...
1k views

### Drawing an dodecahedron with vertexes at given coordinates

I want to draw an (edit)dodecahedron with the vertex in the following coordinates: ...
576 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 ...
673 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, ...
385 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: ...
317 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: ...
528 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-...
370 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: ...
155 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 ...
784 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 ...