VE Primary Great Circle Data


The Vector Equilibrium (VE) (a.k.a. cuboctahedron) has 4 goups of spin axes. These are

  1. 4 triangle face-center-to-face-center axes
  2. 3 square face-center-to-face-center axes
  3. 6 vertex-to-vertex axes
  4. 12 midedge-to-mid-edge axes
for a total of 25 great circles. Each group of axes defines a different set of great circles which criss-cross the surface of the sphere and therefore the faces of the spherical VE as well. Below is an illustration showing a spherical triangle and square face pair criss-crossed with the great circle arcs. The spherical triangle in bold is the LCD spherical triangle. (More on this below.)

Below I show which axis group grenerates which great circle arcs across the VE's faces. The bold arcs are generated by the associated axis group as labeled.

The surface of the spherical VE can be covered by 24 "positive" and 24 "negative" (total = 48) spherical triangles known as the VE LCD spherical triangle. This is the spherical triangle shown in bold in the illustration below.

Now for the tables of the spherical VE's LCD spherical triangle angles.

All angles are given in degrees.

VE's Spherical Surface LCD Angular Data
LABEL ANGLE Q.M.Equ.
BAC 30.000 000 000acos(3,3)
CAD 30.000 000 000acos(3,3)
ABC 90.000 000 000acos(0,1)
CBE 90.000 000 000acos(0,1)
ACB 61.874 494 298acos(4,8)
ACD118.125 505 702180-acos(4,8)
BCF118.125 505 702180-acos(4,8)
DCF 61.874 494 298acos(4,8)
ADC 35.264 389 683acos(2,2)
CDF 19.471 220 634acos(8,8)
FDG 35.264 389 683acos(2,2)
BEF 73.221 345 119acos(1,3)
FEG 33.557 309 762asin(55,99)
GEH 73.221 345 119acos(1,3)
CFD 99.594 068 22790+acos(35,35)
CFE 80.405 931 773asin(35,35)
DFG 80.405 931 773asin(35,35)
EFG 99.594 068 22790+acos(35,35)
DGF 65.905 157 448acos(1,2)
EGF 48.189 685 104asin(60,80)
EGH 65.905 157 448acos(1,2)
EHG 45.000 000 000acos(1,1)

VE's LCD Central Angle Data
LABEL ANGLE Q.M.Equ.
AB 19.471 220 634acos(8,8)
AC 22.207 654 299acos(6,6)
AD 35.264 389 683acos(2,2)
BC 10.893 394 649acos(27,27)
BE 10.024 987 862asin(2,11)
CD 19.106 605 351asin(9,27)
CF 6.353 170 919
DF 17.023 866 185asin(6,20)
DG 18.434 948 823acos(9,9)
EF 14.458 287 920
EG 19.286 325 411acos(42,44)
EH 25.239 401 821acos(4.5,4.5)
FG 10.670 695 266
GH 26.565 051 177acos(4,4)
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