general variant of expanded decachoron,
general variant of expandedbideca
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- general polytopal classes:
- isogonal
links
| Acronym | sobcated |
| Name | small bicuntitruncateddecachoron, general variant of expanded decachoron, general variant of expandedbideca |
| Net |
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| Circumradius | sqrt[(2a2+3ab+3b2+2ac+4bc+3c2)/5] |
| Face vector | 120, 360, 380, 140 |
| Confer |
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| External links | |
This isogonal polychoron cannot be made uniform, i.e. having all 4 edge types at the same size.It occurs as theStott expansion either ofdeca (a=d=0, b=c)or its dualbideca (b=c=0), then surely being bound to b=c and hence d=a sqrt(3/5).Accordingly then the trapezia bc&#d clearly would be rectangles only and thetuts always are uniform.But that form can even be genaralized as described below, i.e. with b and c using independent edge sizes.
Note the general restriction c/sqrt(3) = r(c3o) < r(a3b) = sqrt[(a2+ab+b2)/3] mentioned below.That one assures that the triangles.. .. c.3o. always are farer from the centerthan the parallel hexagons.. .. .b3.a, so that the latter become pseudo faces only andhence don't occur here.
Several other polychora would occur as special cases, although as degenerate cases only as some edge sizes become zero.Accordingly in the respective incidence matrices not only several elements would vanish, but also several countswould be different, due to coincidences. Thence cf. to the individual pages then. Such examples are:deca (a=d=0, b=c),bited (c=0),apid (a=c=0),bideca (b=c=0),respid (b=0, a=2c),bimted (a=0), ...
Incidence matrix according toDynkin symbol
ao3bc3cb3oa&#zd → height = 0 case: c/sqrt(3) = r(c3o) < r(a3b) = sqrt[(a2+ab+b2)/3] d = sqrt[(3a2+2a(b-c)+2(b-c)2)/5](d-lacedtegum sum of 2 inverted (a,b,c)-grips)o.3o.3o.3o. & | 120 | 1 1 2 2 | 2 2 1 3 4 | 1 1 3 1 2------------------+-----+---------------+------------------+---------------a. .. .. .. & | 2 | 60 * * * | 2 0 0 2 0 | 1 0 2 1 0 a.. b. .. .. & | 2 | * 60 * * | 0 2 0 0 2 | 0 1 1 0 2 b.. .. c. .. & | 2 | * * 120 * | 1 1 1 0 1 | 1 1 1 0 1 coo3oo3oo3oo&#d | 2 | * * * 120 | 0 0 0 2 2 | 0 0 2 1 1 d------------------+-----+---------------+------------------+---------------a. .. c. .. & | 4 | 2 0 2 0 | 60 * * * * | 1 0 1 0 0.. b.3c. .. & | 6 | 0 3 3 0 | * 40 * * * | 0 1 0 0 1.. .. c.3o. & | 3 | 0 0 3 0 | * * 40 * * | 1 1 0 0 0ao .. .. ..&#d & | 3 | 1 0 0 2 | * * * 120 * | 0 0 1 1 0.. bc .. ..&#d & | 4 | 0 1 1 2 | * * * * 120 | 0 0 1 0 1------------------+-----+---------------+------------------+---------------a. .. c.3o. & | 6 | 3 0 6 0 | 3 0 2 0 0 | 20 * * * *trip variant.. b.3c.3o. & | 12 | 0 6 12 0 | 0 4 4 0 0 | * 10 * * *tut variantao .. cb ..&#d & | 6 | 2 1 2 4 | 1 0 0 2 2 | * * 60 * *2cup variant (wedge)ao .. .. oa&#d | 4 | 2 0 0 4 | 0 0 0 4 0 | * * * 30 *2ap.. bc3cb ..&#d | 12 | 0 6 6 6 | 0 2 0 0 6 | * * * * 20ditra
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