Square dipyramid (EntityTopic, 16)
From Hi.gher. Space
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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}} | ||
| + | == Geometry == | ||
| + | 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]]. | ||
| + | |||
| + | 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}}. | ||
| + | |||
| + | === Equations === | ||
| + | *Variables: | ||
| + | <blockquote>''l'' ⇒ length of each line in the square dipyramid</blockquote> | ||
| + | |||
| + | *The [[hypervolume]]s of a square dipyramid are given by: | ||
| + | <blockquote>total edge length = 13''l''<br> | ||
| + | total surface area = ''l''<sup>2</sup>(1 + 6√3)<br> | ||
| + | surcell volume = ''l''<sup>2</sup>3<sup>-1</sup>√3 + ''l''<sup>3</sup>3<sup>-1</sup>√2<br> | ||
| + | bulk = ''Unknown''</blockquote> | ||
| + | |||
| + | *The [[realmic]] [[cross-section]]s (''n'') of a square dipyramid are: | ||
| + | <blockquote>[!x,!y] ⇒ [[triangular prism]]<br> | ||
| + | [!z,!w] ⇒ square pyramid</blockquote> | ||
| + | |||
| + | === Net === | ||
| + | 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. | ||
| + | |||
| + | <blockquote>''No image''</blockquote> | ||
| + | |||
| + | == Projection == | ||
| + | The parallel projection of a square dipyramid is the following: | ||
| + | |||
| + | <blockquote>http://fusion-global.org/share/square_dipyramid.png</blockquote> | ||
| + | |||
| + | {{Polychora}} | ||
| + | {{Rotope Nav|17|18|19|II'I<br>Square pyramidal prism|<nowiki>II''</nowiki><br>Square dipyramid|(II'I)<br>Square pyramidal torus|chora}} | ||
Revision as of 20:08, 9 August 2007
Geometry
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.
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(?).
Equations
- Variables:
l ⇒ length of each line in the square dipyramid
- The hypervolumes of a square dipyramid are given by:
total edge length = 13l
total surface area = l2(1 + 6√3)
surcell volume = l23-1√3 + l33-1√2
bulk = Unknown
- The realmic cross-sections (n) of a square dipyramid are:
[!x,!y] ⇒ triangular prism
[!z,!w] ⇒ square pyramid
Net
The net of a square dipyramid is two square based pyramids attached at their bases with four tetrahedrons each attached to another face of one of the square based pyramids.
No image
Projection
The parallel projection of a square dipyramid is the following:
http://fusion-global.org/share/square_dipyramid.png
