Non-Regular Toroidal Solids

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Pentagonal Trapezohedron Toroid
Vertices:  30  (10[3] + 10[3] + 10[4])
Faces:20  ({10 * 2} mirror-symmetric pentagons)
Edges:50  (5 different lengths)
Symmetry:  5-fold Antiprismatic  (D5v)
(values below based on long edge length = 1)
Edge 1 (10):  (5−sqrt(5))/10    ≈0.27639320225002103036
Edge 2 (10):  (3−sqrt(5))/2    ≈0.38196601125010515180
Edge 3 (10):  (sqrt(5)−1)/2    ≈0.61803398874989484820
Edge 4 (10):  (5+sqrt(5))/10    ≈0.72360679774997896964
Edge 5 (10):  1
Volume:(8*sqrt(5)−5)/15    ≈0.859236254666554504752