Questions tagged [polyhedra]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
0answers
27 views

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): ...
5
votes
1answer
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 ...
1
vote
1answer
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 $n$-...
3
votes
2answers
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: ...
2
votes
0answers
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 ...
2
votes
1answer
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: <...
1
vote
1answer
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?
1
vote
1answer
72 views

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-...
0
votes
0answers
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 ...
2
votes
1answer
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 ...
5
votes
3answers
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 (...
1
vote
1answer
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 ...
2
votes
1answer
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 ...
2
votes
1answer
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: ...
2
votes
2answers
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
2
votes
4answers
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.
2
votes
2answers
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: ...
2
votes
1answer
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....
3
votes
1answer
90 views

Rotate PolyhedronData

I'd like to create a Graphics3D rendering of a rotated Polyhedron taken from PolyhedronData[] ...
2
votes
0answers
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 ...
1
vote
1answer
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\\ ...
8
votes
1answer
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 ...
1
vote
0answers
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: ...
1
vote
0answers
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 ...
5
votes
1answer
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....
3
votes
0answers
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 ...
1
vote
0answers
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?
2
votes
2answers
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: ...
9
votes
4answers
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 ...
3
votes
1answer
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,...
0
votes
1answer
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"]
0
votes
0answers
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 ...
-2
votes
1answer
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"] ...
19
votes
0answers
585 views

How to automatically pack irregular polyhedra [closed]

We get the tetrakaidecahedron like this: ...
32
votes
4answers
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 ...
4
votes
1answer
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 ...
3
votes
1answer
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: ...
8
votes
6answers
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 ...
46
votes
1answer
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 ...
0
votes
1answer
1k views

Drawing an dodecahedron with vertexes at given coordinates

I want to draw an (edit)dodecahedron with the vertex in the following coordinates: ...
5
votes
2answers
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 ...
5
votes
1answer
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, ...
4
votes
2answers
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: ...
5
votes
1answer
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: ...
4
votes
2answers
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-...
6
votes
2answers
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: ...
1
vote
1answer
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 ...
9
votes
2answers
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 ...
10
votes
3answers
1k 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
640 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: ...