Wolfram Cloud Document

ThreeD[4]

{1{17,1,14},17{1,17,19},33{49,1,40},49{1,49,57},5{49,22,14},21{1,6,19},37{17,22,40},53{1,38,57},9{17,43,14},25{1,59,19},41{49,43,40},57{1,27,57},13{49,64,14},29{1,48,19},45{17,64,40},61{1,16,57},2{6,1,14},18{22,49,19},34{38,1,40},50{22,17,57},6{38,22,14},22{22,38,19},38{6,22,40},54{22,6,57},10{6,43,14},26{22,27,19},42{38,43,40},58{22,59,57},14{38,64,14},30{22,16,19},46{6,64,40},62{22,48,57},3{59,1,14},19{43,17,19},35{27,1,40},51{43,49,57},7{27,22,14},23{43,6,19},39{59,22,40},55{43,38,57},11{59,43,14},27{43,59,19},43{27,43,40},59{43,27,57},15{27,64,14},31{43,48,19},47{59,64,40},63{43,16,57},4{48,1,14},20{64,49,19},36{16,1,40},52{64,17,57},8{16,22,14},24{64,38,19},40{48,22,40},56{64,6,57},12{48,43,14},28{64,27,19},44{16,43,40},60{64,59,57},16{16,64,14},32{64,16,19},48{48,64,40},64{64,48,57}}

Show[NeighborsPicture[%]];

TrivalentQ[%55]

False

x

ThreeD[{4,4,4}]

{1{17,1,14},17{1,17,19},33{49,1,40},49{1,49,57},5{49,22,14},21{1,6,19},37{17,22,40},53{1,38,57},9{17,43,14},25{1,59,19},41{49,43,40},57{1,27,57},13{49,64,14},29{1,48,19},45{17,64,40},61{1,16,57},2{6,1,14},18{22,49,19},34{38,1,40},50{22,17,57},6{38,22,14},22{22,38,19},38{6,22,40},54{22,6,57},10{6,43,14},26{22,27,19},42{38,43,40},58{22,59,57},14{38,64,14},30{22,16,19},46{6,64,40},62{22,48,57},3{59,1,14},19{43,17,19},35{27,1,40},51{43,49,57},7{27,22,14},23{43,6,19},39{59,22,40},55{43,38,57},11{59,43,14},27{43,59,19},43{27,43,40},59{43,27,57},15{27,64,14},31{43,48,19},47{59,64,40},63{43,16,57},4{48,1,14},20{64,49,19},36{16,1,40},52{64,17,57},8{16,22,14},24{64,38,19},40{48,22,40},56{64,6,57},12{48,43,14},28{64,27,19},44{16,43,40},60{64,59,57},16{16,64,14},32{64,16,19},48{48,64,40},64{64,48,57}}

TrivalentQ[%]

False

Position[%59,49]

{{3,2,1},{4,1},{4,2,2},{5,2,1},{11,2,1},{13,2,1},{18,2,2},{36,2,2},{50,2,2}}

Length[%]

9