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Noble Polytopes

Noble polytopes are defined to have both, vertices and facets are all alike each (isogoal and isohedral, even so the stem -hedr- here seems to be a missnomer with respect to higher dimensions). Thus especially any regular polytope is a noble polytope as well. But there are others too. It is clear therefrom, that the dual of a noble polytope always is a noble polytope as well. – In terms of incidence matrices those define to have just a single row within both the top-most and the bottom-most blocks.

Within the following listing we restrict further to at least scaliform ones in addition. – Ones neither marked regular nor scaliform would be uniform.


---- 3D ----

Noble Polyhedron Facet Count Facet Type General Classes Circumradius
tet4{3}regular convex0.612372
cube6{4}regular convex0.866025
oct8{3}regular convex0.707107
doe12{5}regular convex1.401259
gadregular0.951057
sissid{5/2}regular0.587785
gissidregular0.535233
ike20{3}regular convex0.951057
gikeregular0.587785
euclidean tilings
trat{3}regular convex
squat{4}regular convex
hexat{6}regular convex
hyperbolic tilings
x3o7o{3}regular convex0.873057 i
x3o8oregular convex0.594604 i
x3o∞oregular convex0 i
x4o5o{4}regular convex0.747674 i
x4o6oregular convex0.5 i
x4o8oregular convex0.321797 i
x4o∞oregular convex0 i
x5o4o{5}regular convex0.899454 i
x5o5oregular convex0.528686 i
x5o10oregular convex0.206652 i
x6o4o{6}regular convex0.707107 i
x6o6oregular convex0.353553 i
x7o3o{7}regular convex1.742610 i
x8o3o{8}regular convex1.345608 i
x8o4oregular convex0.594604 i
x8o8oregular convex0.227545 i
x10o5o{10}regular convex0.154508 i
x∞o3o{∞}regular convex0.866025 i
x∞o4oregular convex0.5 i
x∞o∞oregular convex0 i
...

---- 4D ----

Noble Polychoron Facet Count Facet Type General Classes Circumradius
pen5tetregular convex0.632456
triddip6tripconvex0.816497
tes8cuberegular convex1
deca10tutconvex1.414214
pedippipconvex1.203002
stardipstip 0.743496
hiddip12hipconvex1.414214
hedip14hepconvex1.629715
odip16opconvex1.847759
stodipstop 0.765367
hextetregular convex0.707107
dadip20dipconvex2.288246
staddipstiddip 0.874032
twaddip24twipconvex2.732051
icooctregular convex1
cont48ticconvex3.414214
sircsroh 1.847759
bidexteddiscaliform convex1.618034
afficcotcofissary1.414214
gircgroh 0.765367
birgaxtargiscaliform0.618034
gicquith 0.585786
hi120doeregular convex3.702459
sriphisird 3.077684
sitphitigidfissary2.288246
mriphisiddy 1.902113
gahidoeregular1.618034
gohigadregular
fixikeregular
sisppap 
griphigiddy 1.175571
idhiditdid 1
gaghigadregular
paphackipip 
sishisissidregular
paphickistip 
gitphiquitsissidfissary0.874032
graphigird 0.726543
gofixgikeregular0.618034
gishigissidregular
gashisissidregular
gispstarp 
gogishigissidregular0.540182
spysp240peppyscaliform1.618034
stodsap2-pap-blendscaliform
gypaspstappyscaliform0.618034
gatodsap2-starp-blendscaliform
ex600tetregular convex1.618034
gaxtetregular0.618034
gastakix3600tupipfissary scaliform3.077684
sistakixtustipfissary scaliform0.726543
{n},{n}-dip2n{n}-pconvex...
{n/d},{n/d}-dip{n/d}-pconvex...
...
euclidean honeycombs
choncuberegular convex
hiphhipconvex
batchtoeconvex
tiphtripconvex
...
hyperbolic honeycombs
o3x5x3otidconvex2.910693 i
x3x4x3x4*agircoconvex2.197368 i
o3x6x3otoxatconvex2.075910 i
x3x5x3x5*agridconvex1.798907 i
o5x3x5oticonvex
o4x4x4otosquatconvex1.553774 i
x6o3o3ohexatregular convex1.414214 i
x5o3o4odoeregular convex0.899454 i
x6o3o4ohexatregular convex0.707107 i
x4o4o3osquatregular convex
lamina-truncate x4x3o8oticconvex0.594604 i
x4o3o5ocuberegular convex0.555893 i
x3o5o3oikeregular convex0.509376 i
x5o3o5odoeregular convex0.427486 i
x8o4o3ox8o4oregular convex0.400236 i
x6o3o5ohexatregular convex0.381966 i
x10o5o3ox10o5oregular convex0.202376 i
x4o3o6ocuberegular convex0 i
x3o4o4ooctregular convex
x4o4o4osquatregular convex
x3o6o3otratregular convex
...

---- 5D ----

Noble Polyteron Facet Count Facet Type General Classes Circumradius
hix6penregular convex0.645497
pent10tesregular convex1.118034
dot12rapconvex0.866025
hit16pinnip 0.790569
nat32garpop 1.224745
tacpenregular convex0.707107
...
euclidean tetracombs
otcypitgippidconvex
hexthexregular convex
icoticoregular convex
testtesregular convex
tribbittriddipconvex
...
hyperbolic tetracombs
x5o3o3o3ohiregular convex2.301105 i
x5o3o3o4ohiregular convex0.899454 i
o5o3x3o5oroxconvex0.747674 i
x4o3o4o3ochonregular convex0.5 i
x3o3o5o5/2oexregular0.393076 i
x3o5o5/2o5ofixregular
x5o5/2o5o3ogohiregular
x3o3o3o5openregular convex
x5/2o5o3o3osishiregular0.242934 i
x4o3o3o5otesregular convex
x5o3o3o5ohiregular convex0.206652 i
x3o4o3o4oicoregular convex0 i
...


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