Stauroperihedron (EntityTopic, 11)

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Revision as of 11:18, 26 August 2012

The stauroperihedron, also known as the (small) rhombicuboctahedron and cuboctahedral rectate, abbreviated here as COR, is a uniform polyhedron which can be seen as a 3-dimensional analog of the octagon. The other possible analog is the cubic truncate (CT). While the CT has the octagons on the surface of the shape, the COR has them embedded inside it. Thus when one is concerned with powertopes, the COR comprises three "long and thin" cuboids whereas the CT comprises three "wide and flat" cuboids.

For a figure centred at the origin, with edge length 2, its 24 = 3×2³ vertices can be given as all permutations of

〈±1, ±1, ±(1+√2)〉.

As such, the most obvious 4D analog is the stauroperichoron.

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 '''cuboctahedral rectate''' (also known as the '''(small) rhombicuboctahedron''', abbreviated here as '''COR''') is a uniform polyhedron which can be seen as a 3-dimensional analog of the [[octagon]]. The other possible analog is the [[cubic truncate]] (''CT''). While the CT has the octagons on the surface of the shape, the COR has them embedded inside it. Thus when one is concerned with [[powertopes]], the COR comprises three "long and thin" cuboids whereas the CT comprises three "wide and flat" cuboids.
+The '''stauroperihedron''', also known as the '''(small) rhombicuboctahedron''' and '''cuboctahedral rectate''', abbreviated here as '''COR''', is a uniform polyhedron which can be seen as a 3-dimensional analog of the [[octagon]]. The other possible analog is the [[cubic truncate]] (''CT''). While the CT has the octagons on the surface of the shape, the COR has them embedded inside it. Thus when one is concerned with [[powertopes]], the COR comprises three "long and thin" cuboids whereas the CT comprises three "wide and flat" cuboids.
 For a figure centred at the origin, with edge length 2, its 24 = 3×2<sup>3</sup> vertices can be given as all permutations of