Code covered by the BSD License

# geom3d

### David Legland (view profile)

19 Jun 2009 (Updated )

Library to handle 3D geometric primitives: create, intersect, display, and make basic computations

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

createTetrakaidecahedron()
```function varargout = createTetrakaidecahedron()
%CREATETETRAKAIDECAHEDRON Create a 3D mesh representing a tetrakaidecahedron
%
%   [V E F] = createTetrakaidecahedron;
%   Create a mesh structure representing a tetrakaidecahedron, composed of
%   both square and hexagonal faces. Tetrakaidecahedron can be used to tile
%   the 3D Euclidean space.
%
%   V is a 24-by-3 array with vertex coordinates,
%   E is a 36-by-2 array containing indices of neighbour vertices,
%   F is a 14-by-1 cell array containing vertex indices array of each face.
%
%   [V F] = createTetrakaidecahedron;
%   Returns only the vertices and the face vertex indices.
%
%   MESH = createTetrakaidecahedron;
%   Returns the data as a mesh structure, with fields 'vertices', 'edges'
%   and 'faces'.
%
%   Example
%   [n e f] = createTetrakaidecahedron;
%   drawMesh(n, f);
%
%   meshes3d, drawMesh
%
%   ---------
%   author : David Legland
%   INRA - TPV URPOI - BIA IMASTE
%   created the 10/02/2005.
%

%   HISTORY
%   04/01/2007: remove unused variables

nodes = [...
1 0 2;0 1 2;-1 0 2;0 -1 2;...
2 0 1;0 2 1;-2 0 1;0 -2 1;...
2 1 0;1 2 0;-1 2 0;-2 1 0;-2 -1 0;-1 -2 0;1 -2 0;2 -1 0;...
2 0 -1;0 2 -1;-2 0 -1;0 -2 -1;...
1 0 -2;0 1 -2;-1 0 -2;0 -1 -2];

edges = [...
1 2;1 4;1 5;2 3;2 6;3 4;3 7;4 8;...
5 9;5 16;6 10;6 11;7 12;7 13;8 14;8 15;...
9 10;9 17;10 18;11 12;11 18;12 19;13 14;13 19;14 20;15 16;15 20;16 17;....
17 21;18 22;19 23;20 24;21 22;21 24;22 23;23 24];

faces = {...
[1 2 3 4], ...
[1 4 8 15 16 5], [1 5 9 10 6 2], [2 6 11 12 7 3], [3 7 13 14 8 4],...
[5 16 17 9], [6 10 18 11], [7 12 19 13], [8 14 20 15],...
[9 17 21 22 18 10], [11 18 22 23 19 12], [13 19 23 24 20 14], [15 20 24 21 17 16], ...
[21 24 23 22]};
faces = faces';

% format output
varargout = formatMeshOutput(nargout, nodes, edges, faces);

```