1 0 .594603557501360532
-1 0 .594603557501360532
0 1 .594603557501360532
0 -1 .594603557501360532
.707106781186547525 .707106781186547525 -.594603557501360532
.707106781186547525 -.707106781186547525 -.594603557501360532
-.707106781186547525 .707106781186547525 -.594603557501360532
-.707106781186547525 -.707106781186547525 -.594603557501360532

Twisted cube or square antiprism.
The two numbers are 1/sqrt(2) and 1/2^(3/4).
Edge length = sqrt(2).