Rhodomesohedron (EntityTopic, 11)

From Hi.gher. Space

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Revision as of 22:18, 16 February 2014

The rhodomesohedron is the mesotruncate of the dodecahedron and icosahedron. It is also called the icosidodecahedron, which is an interesting name as it represents both the number of faces in the polyhedron (icosidodeca = 32) and also the combination of the two regular polytopes that can be rectified to form it (icosahedron + dodecahedron).

Incidence matrix

Dual: rhombic triacontahedron

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

Usage as facets

24× 1-facets of a rectified snub demitesseract
1× 1-facets of a D4.7

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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 The '''rhodomesohedron''' is the [[mesotruncate]] of the [[dodecahedron]] and [[icosahedron]]. It is also called the '''icosidodecahedron''', which is an interesting name as it represents both the number of faces in the polyhedron ('''icosidodeca''' = 32) and also the combination of the two [[regular polytope]]s that can be [[rectified]] to form it ('''icosa'''hedron + '''dodeca'''hedron).
+<[#polytope [id 20]]>
 {{Trishapes}}