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3D parametric surface: Klein bottle
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<iframe 
    src="http://jsxgraph.org/share/iframe/3d-parametric-surface-klein-bottle" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: 3D parametric surface: Klein bottle" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    var board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-8, 8, 8, -8],
        keepaspectratio: false,
        axis: false
    });
    
    var view = board.create('view3d',
        [
            [-6, -3],
            [8, 8],
            [
                [-5, 5],
                [-5, 5],
                [-5, 5]
            ]
        ], {});
    
    var b = board.create('slider', [[-7, -6], [5, -6], [-3, 2, 4]], {name: 'b'});
    
    // Klein bottle
    var c = view.create('parametricsurface3d', [
        (u, v) => b.Value() * (1 - Math.sin(u)) * Math.cos(u) + (2 - Math.cos(u)) * Math.cos(v) * (2 * Math.exp(-Math.pow(u / 2 - Math.PI, 2)) - 1),
        (u, v) => (2 - Math.cos(u)) * Math.sin(v),
        (u, v) => 4 * Math.sin(u) + 0.5 * (2 - Math.cos(u)) * Math.sin(u) * Math.cos(v) * Math.exp(-Math.pow(u - 3 * Math.PI / 2, 2)),
        [0, 2 * Math.PI],
        [0, 2 * Math.PI],
    ], {
        strokeColor: 'green',
        stepsU: 60,
        stepsV: 60
    });
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

var board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-8, 8, 8, -8],
    keepaspectratio: false,
    axis: false
});

var view = board.create('view3d',
    [
        [-6, -3],
        [8, 8],
        [
            [-5, 5],
            [-5, 5],
            [-5, 5]
        ]
    ], {});

var b = board.create('slider', [[-7, -6], [5, -6], [-3, 2, 4]], {name: 'b'});

// Klein bottle
var c = view.create('parametricsurface3d', [
    (u, v) => b.Value() * (1 - Math.sin(u)) * Math.cos(u) + (2 - Math.cos(u)) * Math.cos(v) * (2 * Math.exp(-Math.pow(u / 2 - Math.PI, 2)) - 1),
    (u, v) => (2 - Math.cos(u)) * Math.sin(v),
    (u, v) => 4 * Math.sin(u) + 0.5 * (2 - Math.cos(u)) * Math.sin(u) * Math.cos(v) * Math.exp(-Math.pow(u - 3 * Math.PI / 2, 2)),
    [0, 2 * Math.PI],
    [0, 2 * Math.PI],
], {
    strokeColor: 'green',
    stepsU: 60,
    stepsV: 60
});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="3D parametric surface: Klein bottle" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   var board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-8, 8, 8, -8],
       keepaspectratio: false,
       axis: false
   });
   
   var view = board.create('view3d',
       [
           [-6, -3],
           [8, 8],
           [
               [-5, 5],
               [-5, 5],
               [-5, 5]
           ]
       ], {});
   
   var b = board.create('slider', [[-7, -6], [5, -6], [-3, 2, 4]], {name: 'b'});
   
   // Klein bottle
   var c = view.create('parametricsurface3d', [
       (u, v) => b.Value() * (1 - Math.sin(u)) * Math.cos(u) + (2 - Math.cos(u)) * Math.cos(v) * (2 * Math.exp(-Math.pow(u / 2 - Math.PI, 2)) - 1),
       (u, v) => (2 - Math.cos(u)) * Math.sin(v),
       (u, v) => 4 * Math.sin(u) + 0.5 * (2 - Math.cos(u)) * Math.sin(u) * Math.cos(v) * Math.exp(-Math.pow(u - 3 * Math.PI / 2, 2)),
       [0, 2 * Math.PI],
       [0, 2 * Math.PI],
   ], {
       strokeColor: 'green',
       stepsU: 60,
       stepsV: 60
   });
</jsxgraph>

3D parametric surface: Klein bottle

3D
A parametric surface is defined by a function $f: {\mathbb R}^2 \to {\mathbb R}^3, \; (u,v) \mapsto (f_x(u,v), f_y(u,v), f_z(u,v))$.
Have also a look at the examples 
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-8, 8, 8, -8],
    keepaspectratio: false,
    axis: false
});

var view = board.create('view3d',
    [
        [-6, -3],
        [8, 8],
        [
            [-5, 5],
            [-5, 5],
            [-5, 5]
        ]
    ], {});

var b = board.create('slider', [[-7, -6], [5, -6], [-3, 2, 4]], {name: 'b'});

// Klein bottle
var c = view.create('parametricsurface3d', [
    (u, v) => b.Value() * (1 - Math.sin(u)) * Math.cos(u) + (2 - Math.cos(u)) * Math.cos(v) * (2 * Math.exp(-Math.pow(u / 2 - Math.PI, 2)) - 1),
    (u, v) => (2 - Math.cos(u)) * Math.sin(v),
    (u, v) => 4 * Math.sin(u) + 0.5 * (2 - Math.cos(u)) * Math.sin(u) * Math.cos(v) * Math.exp(-Math.pow(u - 3 * Math.PI / 2, 2)),
    [0, 2 * Math.PI],
    [0, 2 * Math.PI],
], {
    strokeColor: 'green',
    stepsU: 60,
    stepsV: 60
});

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.