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| - | {{Shape|Square dipyramid|''No image''|4|6, 13, 13, 6|0|N/A|N/A|[[Line (object)|E]][[Square|E]][[Square pyramid|T]]T|11<sup>11</sup> xy<sup>zw</sup>|N/A|N/A|N/A|18|N/A|N/A|pure}}
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| - | == Geometry ==
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| - | A '''square dipyramid''' is a special case of the [[tetrapyramid]] where the base is a [[square pyramid]]. It is also a special case of the [[dipyramid]] where the base is a [[square]].
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| - | The square dipyramid is interesting because the numbers of elements it has (6, 13, 13, 6) are symmetrical, however, since the shape is not [[regular]] it cannot have a [[dual]]. If duals were defined for irregular shapes, this shape may be a self-dual{{hmm}}.
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| - | === Equations ===
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| - | *Variables:
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| - | <blockquote>''l'' ⇒ length of each line in the square dipyramid</blockquote>
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| - | *The [[hypervolume]]s of a square dipyramid are given by:
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| - | <blockquote>total edge length = 13''l''<br>
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| - | total surface area = ''l''<sup>2</sup>(1 + 6√3)<br>
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| - | surcell volume = ''l''<sup>2</sup>3<sup>-1</sup>√3 + ''l''<sup>3</sup>3<sup>-1</sup>√2<br>
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| - | bulk = ''Unknown''</blockquote>
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| - | *The [[realmic]] [[cross-section]]s (''n'') of a square dipyramid are:
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| - | <blockquote>[!x,!y] ⇒ [[triangular prism]]<br>
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| - | [!z,!w] ⇒ square pyramid</blockquote>
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| - | === Net ===
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| - | The net of a square dipyramid is two square based pyramids attached at their bases with four [[tetrahedron]]s each attached to another face of one of the square based pyramids.
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| - | <blockquote>''No image''</blockquote>
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| - | == Projection ==
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| - | The parallel projection of a square dipyramid is the following:
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| - | <blockquote>http://fusion-global.org/share/square_dipyramid.png</blockquote>
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| - | {{Polychora}}
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| - | {{Rotope Nav|17|18|19|II'I<br>Square pyramidal prism|<nowiki>II''</nowiki><br>Square dipyramid|(II'I)<br>Square pyramidal torus|chora}}
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