Acronym	mort
Name	medial rhombic triacontahedron
VRML	⭳ ©
Circumradius wrt. outer vertices	sqrt[(5+sqrt(5))/6] = 1.098185
Circumradius wrt. inner vertices	sqrt[(5-sqrt(5))/6] = 0.678716
Inradius	1/sqrt(3) = 0.577350
Vertex figure	[r5]/2, [R5]
Dihedral angles	at edge:   120°
Dual	did
Face vector	24, 60, 30
Confer	general polytopal classes: Catalan polyhedra
External links

The rhombs {(r,R)²} have vertex angles r = arccos[sqrt(5)/3] = 41.810315° resp. R = arccos[-sqrt(5)/3] = 138.189685°.

Edge size used here is rR = x = 1. This results in rhomb diagonal sizes a = rr = uf/h = [1+sqrt(5)]/sqrt(3) = 1.868345 and b = RR = uv/h = [sqrt(5)-1]/sqrt(3) = 0.713644. The diagonal's ratio of the rhombs here clearly is rr : RR = F = [3+sqrt(5)]/2 = 3.618034.

Incidence matrix according to Dynkin symbol

o5/2m5o =
((ao5/2oo5ob))&#zx   → height = 0
                       a = rr = uf/h = [1+sqrt(5)]/sqrt(3) = 1.868345
                       b = RR = uv/h = [sqrt(5)-1]/sqrt(3) = 0.713644

  o.5/2o.5o.       | 12  * |  5 |  5  [r5]/2
  .o5/2.o5.o       |  * 12 |  5 |  5  [R5]
-------------------+-------+----+---
  oo5/2oo5oo  &#x  |  1  1 | 60 |  2
-------------------+-------+----+---
((ao   .. ob))&#xz |  2  2 |  4 | 30  {(r,R)2}