Pyroteron (EntityTopic, 17)
From Hi.gher. Space
(Difference between revisions)
m (add) |
m (rm "geometry") |
||
| Line 1: | Line 1: | ||
{{Shape|Hexateron|''No image''|5|6, ?, ?, ?, 6|0|{[[Triangle|3,]][[Tetrahedron|3,]][[Pentachoron|3,]]3}|N/A|[[Line (object)|E]][[Triangle|T]][[Tetrahedron|T]][[Pentachoron|T]]T|1<sup>4</sup> x<sup>yzwφ</sup>|[[Pentachoron]], edge 1|N/A|''Self-dual''|89|N/A|N/A|pure|''Unknown''|''Unknown''|(([[Triangle|3]][[Tetrahedron|<sup>3</sup>]])<sup>[[Pentachoron|4]]</sup>)<sup>5</sup>}} | {{Shape|Hexateron|''No image''|5|6, ?, ?, ?, 6|0|{[[Triangle|3,]][[Tetrahedron|3,]][[Pentachoron|3,]]3}|N/A|[[Line (object)|E]][[Triangle|T]][[Tetrahedron|T]][[Pentachoron|T]]T|1<sup>4</sup> x<sup>yzwφ</sup>|[[Pentachoron]], edge 1|N/A|''Self-dual''|89|N/A|N/A|pure|''Unknown''|''Unknown''|(([[Triangle|3]][[Tetrahedron|<sup>3</sup>]])<sup>[[Pentachoron|4]]</sup>)<sup>5</sup>}} | ||
| - | The '''hexateron''' is the 5-dimensional [[simplex]]. | + | The '''hexateron''' is the 5-dimensional [[simplex]]. It is a special case of the [[pyramid]] where the base is a [[pentachoron]]. |
| - | + | == Equations == | |
| - | + | ||
| - | + | ||
| - | + | ||
*Variables: | *Variables: | ||
<blockquote>''l'' ⇒ length of the edges of the hexateron</blockquote> | <blockquote>''l'' ⇒ length of the edges of the hexateron</blockquote> | ||
Revision as of 20:26, 22 September 2007
The hexateron is the 5-dimensional simplex. It is a special case of the pyramid where the base is a pentachoron.
Equations
- Variables:
l ⇒ length of the edges of the hexateron
- All points (x, y, z, w, φ) that lie on the surface of a hexateron will satisfy the following equation:
Unknown
- The hypervolumes of a hexateron are given by:
Unknown
- The flunic cross-sections (n) of a hexateron are:
Unknown
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
