The 12-vertex graph consisting of a cube in which two opposite faces (say, top and bottom) have edges drawn across them which connect the centers of opposite sides of the faces in such a way that the orientation of the edges added on top and bottom are perpendicular to each other.
The bidiakis cube is implemented in the Wolfram Language as GraphData[
"CubicPolyhedral",
4
].
The bidiakis cube is biconnected, cubic, polyhedral, and Hamiltonian.
It has three LCF notations: ![[-6,4,-4]^4](/images/equations/BidiakisCube/Inline3.svg)
, ![[-6,-3,3,-6,3,-3]^2](/images/equations/BidiakisCube/Inline4.svg)
, and ![[-6,-3,3,-6,4,-3,-6,4,-4,-6,3,-4]](/images/equations/BidiakisCube/Inline5.svg)
.
