Coninder (EntityTopic, 11)
From Hi.gher. Space
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[!z] ⇒ [[cylinder]] of radius (''r''-''rnh''<sup>-1</sup>) and height ''l''<br> | [!z] ⇒ [[cylinder]] of radius (''r''-''rnh''<sup>-1</sup>) and height ''l''<br> | ||
[!w] ⇒ cone of base radius ''r'' and height ''h''</blockquote> | [!w] ⇒ cone of base radius ''r'' and height ''h''</blockquote> | ||
| + | |||
| + | == Projection == | ||
| + | The following is the parallel projection of the coninder: | ||
| + | <blockquote>http://fusion-global.org/share/coninder1.png</blockquote> | ||
| + | |||
| + | In perspective projection, the coninder can also appear as two concentric cones. Note that the [[frustum]] at the bottom is actually a cylinder: | ||
| + | <blockquote>http://fusion-global.org/share/coninder2.png</blockquote> | ||
| + | |||
| + | The following are also perspective projections of the coninder. It seems to have four cells: two cones, a cylinder and something else, which may or may not be another cylinder{{hmm}}. | ||
| + | <blockquote>http://fusion-global.org/share/coninder3.png</blockquote> | ||
| + | |||
<br clear="all"><br> | <br clear="all"><br> | ||
{{Polychora}} | {{Polychora}} | ||
{{Rotopes}} | {{Rotopes}} | ||
Revision as of 11:28, 16 June 2007
Geometry
A coninder is a special case of a tetraprism where the base is a cone.
Equations
- Assumption: Coninder's base is centered at the origin.
- Variables:
r ⇒ radius of base of coninder
h ⇒ height of coninder
l ⇒ length of coninder
- The hypervolumes of a coninder are given by:
total edge length = Unknown
total surface area = Unknown
surcell volume = Unknown
bulk = πr2hl3-1
- The realmic cross-sections (n) of a coninder are:
[!x,!y] ⇒ Unknown
[!z] ⇒ cylinder of radius (r-rnh-1) and height l
[!w] ⇒ cone of base radius r and height h
Projection
The following is the parallel projection of the coninder:
http://fusion-global.org/share/coninder1.png
In perspective projection, the coninder can also appear as two concentric cones. Note that the frustum at the bottom is actually a cylinder:
http://fusion-global.org/share/coninder2.png
The following are also perspective projections of the coninder. It seems to have four cells: two cones, a cylinder and something else, which may or may not be another cylinder(?).
http://fusion-global.org/share/coninder3.png
