HgBa2Ca2Cu3O8 crystallizes in the tetragonal P4/mmm space group. Ba(1) is bonded in a 8-coordinate geometry to four equivalent O(2) and four equivalent O(3) atoms. Ca(1) is bonded in a body-centered cubic geometry to four equivalent O(1) and four equivalent O(3) atoms. There are two inequivalent Cu sites. In the first Cu site, Cu(1) is bonded in a rectangular see-saw-like geometry to four equivalent O(3) atoms. In the second Cu site, Cu(2) is bonded in a square co-planar geometry to four equivalent O(1) atoms. Hg(1) is bonded in a linear geometry to two equivalent O(2) atoms. There are three inequivalent O sites. In the first O site, O(1) is bonded to four equivalent Ca(1) and two equivalent Cu(2) atoms to form OCa4Cu2 octahedra that share corners with two equivalent O(1)Ca4Cu2 octahedra, corners with twelve equivalent O(3)Ba2Ca2Cu2 octahedra, edges with two equivalent O(3)Ba2Ca2Cu2 octahedra, edges with two equivalent O(1)Ca4Cu2 octahedra, and faces with four equivalent O(1)Ca4Cu2 octahedra. The corner-sharing octahedral tilt angles range from 0-66°. In the second O site, O(2) is bonded in a 5-coordinate geometry to four equivalent Ba(1) and one Hg(1) atom. In the third O site, O(3) is bonded to two equivalent Ba(1), two equivalent Ca(1), and two equivalent Cu(1) atoms to form distorted OBa2Ca2Cu2 octahedra that share corners with two equivalent O(3)Ba2Ca2Cu2 octahedra, corners with six equivalent O(1)Ca4Cu2 octahedra,  an edgeedge with one O(1)Ca4Cu2 octahedra, edges with two equivalent O(3)Ba2Ca2Cu2 octahedra, and faces with four equivalent O(3)Ba2Ca2Cu2 octahedra. The corner-sharing octahedral tilt angles range from 1-66°.
HgBa2Ca2Cu3O8 crystallizes in the tetragonal P4/mmm space group. Ba(1) is bonded in a 8-coordinate geometry to four equivalent O(2) and four equivalent O(3) atoms. All Ba(1)-O(2) bond lengths are 2.92 Å. All Ba(1)-O(3) bond lengths are 2.75 Å. Ca(1) is bonded in a body-centered cubic geometry to four equivalent O(1) and four equivalent O(3) atoms. All Ca(1)-O(1) bond lengths are 2.53 Å. All Ca(1)-O(3) bond lengths are 2.51 Å. There are two inequivalent Cu sites. In the first Cu site, Cu(1) is bonded in a rectangular see-saw-like geometry to four equivalent O(3) atoms. All Cu(1)-O(3) bond lengths are 1.95 Å. In the second Cu site, Cu(2) is bonded in a square co-planar geometry to four equivalent O(1) atoms. All Cu(2)-O(1) bond lengths are 1.95 Å. Hg(1) is bonded in a linear geometry to two equivalent O(2) atoms. Both Hg(1)-O(2) bond lengths are 2.01 Å. There are three inequivalent O sites. In the first O site, O(1) is bonded to four equivalent Ca(1) and two equivalent Cu(2) atoms to form OCa4Cu2 octahedra that share corners with two equivalent O(1)Ca4Cu2 octahedra, corners with twelve equivalent O(3)Ba2Ca2Cu2 octahedra, edges with two equivalent O(3)Ba2Ca2Cu2 octahedra, edges with two equivalent O(1)Ca4Cu2 octahedra, and faces with four equivalent O(1)Ca4Cu2 octahedra. The corner-sharing octahedral tilt angles range from 0-66°. In the second O site, O(2) is bonded in a 5-coordinate geometry to four equivalent Ba(1) and one Hg(1) atom. In the third O site, O(3) is bonded to two equivalent Ba(1), two equivalent Ca(1), and two equivalent Cu(1) atoms to form distorted OBa2Ca2Cu2 octahedra that share corners with two equivalent O(3)Ba2Ca2Cu2 octahedra, corners with six equivalent O(1)Ca4Cu2 octahedra,  an edgeedge with one O(1)Ca4Cu2 octahedra, edges with two equivalent O(3)Ba2Ca2Cu2 octahedra, and faces with four equivalent O(3)Ba2Ca2Cu2 octahedra. The corner-sharing octahedral tilt angles range from 1-66°.