Coninder (EntityTopic, 11)

From Hi.gher. Space

(Difference between revisions)
m (fix)
m
Line 7: Line 7:
| ssc=[x(yz)P]
| ssc=[x(yz)P]
| ssc2=+&T2
| ssc2=+&T2
-
| extra={{STS Rotope
+
| extra={{STS Tapertope
-
| attrib=pure
+
| order=2, 1
-
| notation=2<sup>1</sup>1
+
| notation=12<sup>1</sup>
-
| index=37
+
| index=24
}}}}
}}}}
Line 45: Line 45:
{{Tetrashapes}}
{{Tetrashapes}}
-
{{Rotope Nav|36|37|38|((II)II)<br>Toracubinder|(II)'I<br>Coninder|<nowiki>(II)''</nowiki><br>Dicone|chora}}
+
{{Tapertope Nav|23|24|25|[11]<sup>2</sup><br>Square dipyramid|12<sup>1</sup><br>Coninder|1[11]<sup>1</sup><br>Square pyramidal prism|chora}}

Revision as of 21:11, 24 November 2009


A coninder is a special case of a prism where the base is a cone. It is bounded by two cones, a cylinder and a cylindrogram.

Equations

  • Variables:
r ⇒ radius of base of coninder
h ⇒ height of coninder
l ⇒ length of coninder
total edge length = 4πr+l
total surface area = 2πr(r+2l+(r2+h2)2-1)
surcell volume = 2πr2(l+h3-1)
bulk = πr2hl3-1
[!x,!y] ⇒ Unknown
[!z] ⇒ cylinder of radius (r-rnh-1) and height l
[!w] ⇒ cone of base radius r and height h

Projections

The following is the parallel projection of the coninder:

http://teamikaria.com/share/?caption=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://teamikaria.com/share/?caption=coninder2.png

The following are also perspective projections of the coninder. It shows the two cones and the cylinder, with the cylindrogram collapsed into a line:

http://teamikaria.com/share/?caption=coninder3.png

Its edge-first projection into 3-space is a cylinder containing two cones joined apex to apex by an edge.


Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus


23. [11]2
Square dipyramid
24. 121
Coninder
25. 1[11]1
Square pyramidal prism
List of tapertopes