I32d_1 Vertex Coordinates Class A radius R: sqrt( (21 - 9 sqrt(5)) / 2 ), approx. 0.661584538250 ( ±1 / sqrt(3), ±1 / sqrt(3), ±1 / sqrt(3) ) * R even permutations of ( ±(sqrt(5) + 1) / 2 sqrt(3), 0, ±(sqrt(5) - 1) / 2 sqrt(3) ) * R A01: 0.38196601125010515180 0.38196601125010515180 0.38196601125010515180 A02: 0.38196601125010515180 0.38196601125010515180 -0.38196601125010515180 A03: 0.38196601125010515180 -0.38196601125010515180 0.38196601125010515180 A04: 0.38196601125010515180 -0.38196601125010515180 -0.38196601125010515180 A05: -0.38196601125010515180 0.38196601125010515180 0.38196601125010515180 A06: -0.38196601125010515180 0.38196601125010515180 -0.38196601125010515180 A07: -0.38196601125010515180 -0.38196601125010515180 0.38196601125010515180 A08: -0.38196601125010515180 -0.38196601125010515180 -0.38196601125010515180 A09: 0.61803398874989484820 0.00000000000000000000 0.23606797749978969641 A10: 0.61803398874989484820 0.00000000000000000000 -0.23606797749978969641 A11: -0.61803398874989484820 0.00000000000000000000 0.23606797749978969641 A12: -0.61803398874989484820 0.00000000000000000000 -0.23606797749978969641 A13: 0.23606797749978969641 0.61803398874989484820 0.00000000000000000000 A14: -0.23606797749978969641 0.61803398874989484820 0.00000000000000000000 A15: 0.23606797749978969641 -0.61803398874989484820 0.00000000000000000000 A16: -0.23606797749978969641 -0.61803398874989484820 0.00000000000000000000 A17: 0.00000000000000000000 0.23606797749978969641 0.61803398874989484820 A18: 0.00000000000000000000 -0.23606797749978969641 0.61803398874989484820 A19: 0.00000000000000000000 0.23606797749978969641 -0.61803398874989484820 A20: 0.00000000000000000000 -0.23606797749978969641 -0.61803398874989484820 Class B radius: 1.0 permutations of ( ±1, 0, 0 ) even permutations of ( ±(sqrt(5) + 1) / 4, ±(sqrt(5) - 1) / 4, ±1 / 2 ) B01: 1.00000000000000000000 0.00000000000000000000 0.00000000000000000000 B02: -1.00000000000000000000 0.00000000000000000000 0.00000000000000000000 B03: 0.00000000000000000000 1.00000000000000000000 0.00000000000000000000 B04: 0.00000000000000000000 -1.00000000000000000000 0.00000000000000000000 B05: 0.00000000000000000000 0.00000000000000000000 1.00000000000000000000 B06: 0.00000000000000000000 0.00000000000000000000 -1.00000000000000000000 B07: 0.80901699437494742410 0.30901699437494742410 0.50000000000000000000 B08: 0.80901699437494742410 -0.30901699437494742410 0.50000000000000000000 B09: 0.80901699437494742410 0.30901699437494742410 -0.50000000000000000000 B10: 0.80901699437494742410 -0.30901699437494742410 -0.50000000000000000000 B11: -0.80901699437494742410 0.30901699437494742410 0.50000000000000000000 B12: -0.80901699437494742410 -0.30901699437494742410 0.50000000000000000000 B13: -0.80901699437494742410 0.30901699437494742410 -0.50000000000000000000 B14: -0.80901699437494742410 -0.30901699437494742410 -0.50000000000000000000 B15: 0.50000000000000000000 0.80901699437494742410 0.30901699437494742410 B16: 0.50000000000000000000 0.80901699437494742410 -0.30901699437494742410 B17: -0.50000000000000000000 0.80901699437494742410 0.30901699437494742410 B18: -0.50000000000000000000 0.80901699437494742410 -0.30901699437494742410 B19: 0.50000000000000000000 -0.80901699437494742410 0.30901699437494742410 B20: 0.50000000000000000000 -0.80901699437494742410 -0.30901699437494742410 B21: -0.50000000000000000000 -0.80901699437494742410 0.30901699437494742410 B22: -0.50000000000000000000 -0.80901699437494742410 -0.30901699437494742410 B23: 0.30901699437494742410 0.50000000000000000000 0.80901699437494742410 B24: -0.30901699437494742410 0.50000000000000000000 0.80901699437494742410 B25: 0.30901699437494742410 -0.50000000000000000000 0.80901699437494742410 B26: -0.30901699437494742410 -0.50000000000000000000 0.80901699437494742410 B27: 0.30901699437494742410 0.50000000000000000000 -0.80901699437494742410 B28: -0.30901699437494742410 0.50000000000000000000 -0.80901699437494742410 B29: 0.30901699437494742410 -0.50000000000000000000 -0.80901699437494742410 B30: -0.30901699437494742410 -0.50000000000000000000 -0.80901699437494742410 Face Cycles Covering Faces A01 B10 A13 B08 A02 B23 A10 B03 A09 B27 A01 B18 A17 B16 A05 B07 A14 B05 A13 B11 A01 B26 A09 B24 A03 B15 A18 B01 A17 B19 A02 B13 A13 B06 A14 B09 A06 B15 A19 B17 A02 B20 A19 B01 A20 B16 A04 B28 A10 B30 A03 B12 A15 B05 A16 B08 A07 B20 A18 B22 A03 B29 A09 B04 A10 B25 A04 B07 A15 B09 A04 B21 A20 B19 A08 B10 A16 B06 A15 B14 A05 B21 A17 B02 A18 B17 A07 B23 A11 B25 A05 B28 A11 B03 A12 B24 A06 B12 A14 B14 A06 B29 A12 B27 A08 B18 A20 B02 A19 B22 A07 B13 A16 B11 A08 B26 A12 B04 A11 B30 Central Faces A01 B10 A08 B11 A01 B18 A08 B19 A01 B26 A08 B27 A02 B08 A07 B13 A02 B17 A07 B20 A02 B23 A07 B30 A03 B09 A06 B12 A03 B15 A06 B22 A03 B24 A06 B29 A04 B07 A05 B14 A04 B16 A05 B21 A04 B25 A05 B28 A09 B03 A12 B04 A09 B24 A12 B29 A09 B26 A12 B27 A10 B03 A11 B04 A10 B23 A11 B30 A10 B25 A11 B28 A13 B05 A16 B06 A13 B08 A16 B13 A13 B10 A16 B11 A14 B05 A15 B06 A14 B07 A15 B14 A14 B09 A15 B12 A17 B01 A20 B02 A17 B16 A20 B21 A17 B18 A20 B19 A18 B01 A19 B02 A18 B15 A19 B22 A18 B17 A19 B20 Face Geometry Edge length (for unit outer radius) sqrt( (23 - 9 sqrt(5)) / 2 ), approx. 1.199038823913 Covering face angles arccos( ( 4 + 11 sqrt(5)) / 31 ), approx. 22.709256184451 degrees arccos( (101 - 9 sqrt(5)) / 124 ), approx. 49.290743815549 degrees Central face angles arccos( (-8 + 9 sqrt(5)) / 31 ), approx. 66.976010257987 degrees arccos( ( 8 - 9 sqrt(5)) / 31 ), approx. 113.023989742013 degrees Dihedral angle arccos( sqrt( (5 - sqrt(5)) / 30 ) ), approx. 72.330192892948 degrees