Acronym	sobcated
Name	small bicuntitruncated decachoron, general variant of expanded decachoron, general variant of expanded bideca
Net	©
Circumradius	sqrt[(2a2+3ab+3b2+2ac+4bc+3c2)/5]
Face vector	120, 360, 380, 140
Confer	general polytopal classes: isogonal
External links

This isogonal polychoron cannot be made uniform, i.e. having all 4 edge types at the same size. It occurs as the Stott expansion either of deca (a=d=0, b=c) or its dual bideca (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 the tuts 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 center than the parallel hexagons .. .. .b3.a, so that the latter become pseudo faces only and hence 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 counts would 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 to Dynkin 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-laced tegum 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  c
oo3oo3oo3oo&#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  0
ao .. .. ..&#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 variant
ao .. 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 |  *  *  *  * 20  ditra