Icosahedron (EntityTopic, 12)

From Hi.gher. Space

(Difference between revisions)

Revision as of 08:23, 18 March 2014

Equations

The hypervolumes of an icosahedron with side length l are given by:

total edge length = 30l
surface area = 5√3 · l²
volume = ^5(3+√5)∕₁₂ · l³

Relation to other polyhedra

Non-convex polyhedra sharing vertex coordinates with the icosahedron can be morphed into J91 (bilbiro) and J92 (thawro) as seen in the following animations:

The above animations are not embedded into the page due to a wiki bug. Please leave them as links and do not embed them.

Incidence matrix

Dual: dodecahedron

#	TXID	Va	Ea	3a	Type	Name
0	Va				= point	;
1	Ea	2			= digon	;
2	3a	3	3		= triangle	;
3	C1a	12	30	20	= icosahedron	;

Usage as facets

6× 1-facets of a tetraaugmented triangular hebesphenorotundaeic rhombochoron

Notable Trishapes
Regular:	tetrahedron • cube • octahedron • dodecahedron • icosahedron
Direct truncates:	tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate
Mesotruncates:	stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron
Snubs:	snub staurohedron • snub rhodohedron
Curved:	sphere • torus • cylinder • cone • frustum • crind

@@ Line 27: / Line 27: @@
 surface area = 5√3 {{DotHV}}<br>
 volume = {{Over|5(3+√5)|12}} {{DotHV|3}}</blockquote>
+== Relation to other polyhedra ==
+Non-convex polyhedra sharing vertex coordinates with the icosahedron can be morphed into J91 ([[bilbiro]]) and J92 ([[thawro]]) as seen in the following animations:
+*[http://hddb.teamikaria.com/dl/VH65013KB0RBM2245X71MWVZY2.gif bilbiro]
+*[http://hddb.teamikaria.com/dl/G6TYPETKGR822V4FPSQYPQ5PEF.gif thawro]
+{{Selfref|The above animations are not embedded into the page due to a wiki bug. Please leave them as links and do not embed them.}}
 <[#polytope [id 5]]>
 {{Trishapes}}