If the lateral pentagons are regular and their edge length is 1, Stella tells me that the other edge length is 4.69217462142686, the acute angle is 29.8878°:
metric data:
28 facelets, of 2 types; 70 edgelets; 44 vertices, of 4 types.
Radius 4.83391, Diameter 9.66782
Facelet type 0: area 1.72048
Edge 0-0: Joins 1-1, Length 1, Dihedral 142.09 deg, Mitre 18.9551 deg
Face angle 108 deg
Edge 0-1: Joins 0-1, Length 1, Dihedral 152.938 deg, Mitre 13.5311 deg
Face angle 108 deg
Edge 0-2: Joins 1-0, Length 1, Dihedral 142.09 deg, Mitre 18.9551 deg
Face angle 108 deg
Edge 0-3: Joins 1-2, Length 1, Dihedral 142.09 deg, Mitre 18.9551 deg
Face angle 108 deg
Edge 0-4: Joins 0-4, Length 1, Dihedral 152.938 deg, Mitre 13.5311 deg
Face angle 108 deg
Facelet type 1: area 6.68965
Edge 1-0: Joins 0-2, Length 1, Dihedral 142.09 deg, Mitre 18.9551 deg
Face angle 135.234 deg
Edge 1-1: Joins 0-0, Length 1, Dihedral 142.09 deg, Mitre 18.9551 deg
Face angle 135.234 deg
Edge 1-2: Joins 0-3, Length 1, Dihedral 142.09 deg, Mitre 18.9551 deg
Face angle 119.822 deg
Edge 1-3: Joins 1-4, Length 4.69217, Dihedral 137.658 deg, Mitre 21.1709 deg
Face angle 29.8878 deg
Edge 1-4: Joins 1-3, Length 4.69217, Dihedral 137.658 deg, Mitre 21.1709 deg
Face angle 119.822 deg
Ulrich