Acronym sladit
Name small lanceal ditriacontahedron,
strombic hexecontahedron,
deltoidal hexecontahedron,
tetragonal hexecontahedron
 
 ©
Inradius sqrt[(97+43 sqrt(5))/82] = 1.534764
Dihedral angles
  • at long edge:   arccos[-(19+8 sqrt(5))/41] = 154.121363°
  • at short edge:   arccos[-(19+8 sqrt(5))/41] = 154.121363°
Dual srid
External
links
wikipedia   polytopewiki   mathworld  

Only the lacings c and d survive as true edges. Those are the long resp. short ones. For their ratio one furthermore derives c/d = (7+sqrt(5))/6 = 1.539345. All other distances given below qualify as pseude edges only. Esp. x is nothing but the girding diagonal of the kites, and e is just the axial diagonal of the kites.


Incidence matrix according to Dynkin symbol

m3o5m =
aoo3oxo5oob&#z(c,d,e)   → height = 0
                          a = (3+sqrt(5))/3 = 1.745356
                          b = (8+2 sqrt(5))/11 = 1.133831
                          c = lacing(1,2) = sqrt[5+sqrt(5)]/3 = 0.896665
                          d = lacing(2,3) = sqrt[50-4 sqrt(5)]/11 = 0.582498
                          e = lacing(1,3) = sqrt[626+250 sqrt(5)]/33 = 1.043154

o..3o..5o..         | 12  *  * |  4  0 |  4
.o.3.o.5.o.         |  * 30  * |  2  2 |  4
..o3..o5..o         |  *  * 20 |  0  3 |  3
--------------------+----------+-------+---
oo.3oo.5oo.&#c      |  1  1  0 | 60  * |  2  c
.oo3.oo5.oo&#d      |  0  1  1 |  * 60 |  2  d
--------------------+----------+-------+---
... oxo ...&#(c,d)t |  1  2  1 |  2  2 | 60

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