Rhodopantohedron (EntityTopic, 11)

From Hi.gher. Space

(Difference between revisions)

Latest revision as of 11:29, 2 March 2014

The rhodopantohedron, also known as the omnitruncated dodecahedron, great rhombicosidodecahedron, rhombitruncated icosidodecahedron and truncated icosidodecahedron, is the omnitruncate of the dodecahedron and icosahedron.

Incidence matrix

Dual: disdyakis triacontahedron

#	TXID	Va	Ea	Eb	Ec	10a	4a	6a	Type	Name
0	Va								= point	;
1	Ea	2							= digon	;
2	Eb	2							= digon	;
3	Ec	2							= digon	;
4	10a	10	5	5	0				= decagon	;
5	4a	4	2	0	2				= square	;
6	6a	6	0	3	3				= hexagon	;
7	C1a	120	60	60	60	12	30	20	= rhodopantohedron	;

Usage as facets

2× 1-facets of a castellated rhodopantohedral prism

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 3: / Line 3: @@
 | dim=3
 | elements=62, 180, 120
+| sym=[[Rhodohedral symmetry|I<sub>h</sub>, H<sub>3</sub>, [5,3], (*532)]]
 | ssc={G5<sup>3</sup>}X7
 | ssc2=Ki7
 | extra={{STS Polytope
 | flayout={{FLD|a2tr|ti|a3tm|ti|a5tl|cr}}
-| altern=[[Snub dodecahedron]]
+| altern=[[Snub rhodohedron]]
 | dual=[[Disdyakis triacontahedron]]
+| bowers=Grid
 }}{{STS Uniform polytope
 | wythoff=<nowiki>2 3 5 |</nowiki>
@@ Line 15: / Line 17: @@
 | vlayout=[[Square|4]]⋅[[Hexagon|6]]⋅[[Decagon|10]]
 | vfigure=[[Triangle]]
-| bowers=Grid
 }}}}
+The '''rhodopantohedron''', also known as the '''omnitruncated dodecahedron''', '''great rhombicosidodecahedron''', '''rhombitruncated icosidodecahedron''' and '''truncated icosidodecahedron''', is the [[omnitruncate]] of the [[dodecahedron]] and [[icosahedron]].
+<[#polytope [id 28]]>
 {{Trishapes}}