Rhodoperihedron (EntityTopic, 11)

From Hi.gher. Space

(Difference between revisions)

Latest revision as of 14:07, 15 March 2014

The rhodoperihedron, also known as the (small) rhombicosidodecahedron, is the peritruncate of the dodecahedron and icosahedron. There are 12 Johnson solids, J₇₂ to J₈₃, which are named after this shape (hence the push for elemental names so that they aren't so ridiculously long).

Incidence matrix

Dual: deltoidal hexecontahedron

#	TXID	Va	Ea	Eb	5a	4a	3a	Type	Name
0	Va							= point	;
1	Ea	2						= digon	;
2	Eb	2						= digon	;
3	5a	5	5	0				= pentagon	;
4	4a	4	2	2				= square	;
5	3a	3	0	3				= triangle	;
6	C1a	60	60	60	12	30	20	= rhodoperihedron	;

Usage as facets

2× 1-facets of a castellated rhodoperihedral 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

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 | vfigure=[[Trapezium]], sides {1, √2, φ, √2}
 }}}}
-The '''rhodoperihedron''', also known as the '''(small) rhombicosidodecahedron''', is the [[peritruncate]] of the [[dodecahedron]] and [[icosahedron]]. There are 12 [[Johnson solids]], J<sub>72</sub> to J<sub>83</sub>, which are named after this shape (hence the push for [[Tamfang name]]s so that they aren't so ridiculously long).
+The '''rhodoperihedron''', also known as the '''(small) rhombicosidodecahedron''', is the [[peritruncate]] of the [[dodecahedron]] and [[icosahedron]]. There are 12 [[Johnson solids]], J<sub>72</sub> to J<sub>83</sub>, which are named after this shape (hence the push for [[elemental name]]s so that they aren't so ridiculously long).
 <[#polytope [id 26]]>
 {{Trishapes}}