Tesseric pyramid (EntityTopic, 11)
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| - | {{Shape|Tesseric pyramid| | + | <[#ontology [kind topic] [cats 5D Tapertope Flat]]> |
| + | {{STS Shape | ||
| + | | name=Tesseric pyramid | ||
| + | | dim=5 | ||
| + | | elements=9, 32, 56, 48, 17 | ||
| + | | genus=0 | ||
| + | | ssc=[xyzw]P | ||
| + | | ssc2=&Ke1 | ||
| + | | extra={{STS Tapertope | ||
| + | | order=4, 1 | ||
| + | | notation=[1111]<sup>1</sup> | ||
| + | | index=41 | ||
| + | }}}} | ||
| + | A '''tesseric pyramid''' is a special case of the [[pyramid]] where the base is a [[tesseract]]. Note that if one attempts to construct a tesseric pyramid with equal edge lengths, the height turns out to be zero and the pyramid is degenerate, due to the distance from the tesseract's vertex to its center being exactly {{Over|√4|2}} = 1 times the edge length. | ||
| - | + | == Equations == | |
| - | + | ||
| - | + | ||
| - | + | ||
*Variables: | *Variables: | ||
<blockquote>''l'' ⇒ length of the edges of the tesseric pyramid</blockquote> | <blockquote>''l'' ⇒ length of the edges of the tesseric pyramid</blockquote> | ||
| Line 18: | Line 28: | ||
{{Pentashapes}} | {{Pentashapes}} | ||
| - | {{ | + | {{Tapertope Nav|40|41|42|[211]<sup>1</sup><br>Cubindrone|[1111]<sup>1</sup><br>Tesseric pyramid|31<sup>1</sup><br>Sphentrianglinder|tera}} |
Latest revision as of 23:05, 11 February 2014
A tesseric pyramid is a special case of the pyramid where the base is a tesseract. Note that if one attempts to construct a tesseric pyramid with equal edge lengths, the height turns out to be zero and the pyramid is degenerate, due to the distance from the tesseract's vertex to its center being exactly √4∕2 = 1 times the edge length.
Equations
- Variables:
l ⇒ length of the edges of the tesseric pyramid
- All points (x, y, z, w, φ) that lie on the surteron of a tesseric pyramid will satisfy the following equation:
Unknown
- The hypervolumes of a tesseric pyramid are given by:
Unknown
- The flunic cross-sections (n) of a tesseric pyramid are:
Unknown
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
| 40. [211]1 Cubindrone | 41. [1111]1 Tesseric pyramid | 42. 311 Sphentrianglinder |
| List of tapertopes | ||
