diff --git a/src/srf/boolean.cpp b/src/srf/boolean.cpp
index 16bd74dd0..4ece8a8d7 100644
--- a/src/srf/boolean.cpp
+++ b/src/srf/boolean.cpp
@@ -203,6 +203,115 @@ SCurve SCurve::MakeCopySplitAgainst(SShell *agnstA, SShell *agnstB,
     return ret;
 }
 
+//-----------------------------------------------------------------------------
+// Insert p as a vertex of the piecewise linear curve sc, if it lies within one
+// of sc's segments (and on sc's exact curve, where we have one) and isn't
+// already one of its points. Returns true if we changed the curve.
+//-----------------------------------------------------------------------------
+static bool InsertVertexIntoCurve(SCurve *sc, Vector p) {
+    for(const SCurvePt &scpt : sc->pts) {
+        if(scpt.p.Equals(p)) return false;
+    }
+
+    int i;
+    for(i = 1; i < sc->pts.n; i++) {
+        Vector a = sc->pts[i-1].p,
+               d = (sc->pts[i].p).Minus(a);
+        double m = d.MagSquared();
+        if(m < LENGTH_EPS*LENGTH_EPS) continue;
+        double t = (p.Minus(a)).Dot(d)/m;
+        if((t <= 0.0) || (t >= 1.0)) continue;
+        if((p.Minus(a.Plus(d.ScaledBy(t)))).Magnitude() > LENGTH_EPS) continue;
+        break;
+    }
+    if(i >= sc->pts.n) return false;
+
+    // The pwl chord of a curved segment is not the curve, so make sure that
+    // the point really lies on the curve and not just near the chord.
+    if(sc->isExact) {
+        double t;
+        sc->exact.ClosestPointTo(p, &t, /*mustConverge=*/false);
+        if((p.Minus(sc->exact.PointAt(t))).Magnitude() > LENGTH_EPS) return false;
+    }
+
+    SCurvePt scpt = {};
+    scpt.p      = p;
+    scpt.vertex = true;
+
+    List<SCurvePt> pts = {};
+    pts.ReserveMore(sc->pts.n + 1);
+    for(int j = 0; j < sc->pts.n; j++) {
+        if(j == i) pts.Add(&scpt);
+        pts.Add(&(sc->pts[j]));
+    }
+    sc->pts.Clear();
+    sc->pts = pts;
+    return true;
+}
+
+//-----------------------------------------------------------------------------
+// A curve of one shell may cross a curve of the other shell at a point that is
+// a vertex of neither input shell, and that lies on no surface which either
+// curve crosses transversally; that happens where the two shells touch without
+// passing through each other, for example where an edge of one runs within a
+// coincident face of the other. MakeCopySplitAgainst() splits curves against
+// surfaces, so at such a point it splits only whichever of the two curves does
+// meet a transversal surface there, and leaves the other one whole. The
+// unsplit curve then contributes a single trim edge whose two halves classify
+// differently, which cannot be represented: the edge is kept or discarded
+// whole, and the trim polygon fails to assemble, so the face is lost.
+//
+// So propagate the splits that we just made. Any vertex that splitting created
+// within a curve from one operand, and that lies within a curve from the other
+// operand, becomes a vertex of that curve too.
+//-----------------------------------------------------------------------------
+void SShell::SplitCurvesAtCrossings() {
+    List<Vector> vert[2] = {};
+    for(SCurve &sc : curve) {
+        int i;
+        if(sc.source == SCurve::Source::A) {
+            i = 0;
+        } else if(sc.source == SCurve::Source::B) {
+            i = 1;
+        } else {
+            continue;
+        }
+        // Only the interior points that a split created; the endpoints of a
+        // curve are its shell's own vertices, and an exact curve's endpoints
+        // may lie outside the real geometry entirely (issue #1452).
+        for(int j = 1; j < sc.pts.n - 1; j++) {
+            if(sc.pts[j].vertex) vert[i].Add(&(sc.pts[j].p));
+        }
+    }
+
+    if(!vert[0].IsEmpty() || !vert[1].IsEmpty()) {
+        for(SCurve &sc : curve) {
+            int i;
+            if(sc.source == SCurve::Source::A) {
+                i = 1;
+            } else if(sc.source == SCurve::Source::B) {
+                i = 0;
+            } else {
+                continue;
+            }
+
+            Vector cmax = {VERY_NEGATIVE, VERY_NEGATIVE, VERY_NEGATIVE},
+                   cmin = {VERY_POSITIVE, VERY_POSITIVE, VERY_POSITIVE};
+            for(const SCurvePt &scpt : sc.pts) {
+                scpt.p.MakeMaxMin(&cmax, &cmin);
+            }
+
+            for(const Vector &p : vert[i]) {
+                if(p.OutsideAndNotOn(cmax, cmin)) continue;
+                InsertVertexIntoCurve(&sc, p);
+            }
+        }
+    }
+
+    vert[0].Clear();
+    vert[1].Clear();
+}
+
 void SShell::CopyCurvesSplitAgainst(bool opA, SShell *agnst, SShell *into) {
 #pragma omp parallel for
     for(int i=0; i<curve.n; i++) {
@@ -859,6 +968,11 @@ void SShell::MakeFromBoolean(SShell *a, SShell *b, SSurface::CombineAs type) {
     a->CopyCurvesSplitAgainst(/*opA=*/true,  b, this);
     b->CopyCurvesSplitAgainst(/*opA=*/false, a, this);
 
+    // Where the two shells touch without crossing, a curve of one shell can
+    // cross a curve of the other at a point that splitting against surfaces
+    // finds on only one of the two curves; carry those points across.
+    SplitCurvesAtCrossings();
+
     // Generate the intersection curves for each surface in A against all
     // the surfaces in B (which is all of the intersection curves).
     a->MakeIntersectionCurvesAgainst(b, this);
diff --git a/src/srf/surface.h b/src/srf/surface.h
index d11716762..81124abc9 100644
--- a/src/srf/surface.h
+++ b/src/srf/surface.h
@@ -402,6 +402,7 @@ class SShell {
     void MakeFromIntersectionOf(SShell *a, SShell *b);
     void MakeFromBoolean(SShell *a, SShell *b, SSurface::CombineAs type);
     void CopyCurvesSplitAgainst(bool opA, SShell *agnst, SShell *into);
+    void SplitCurvesAtCrossings();
     void CopySurfacesTrimAgainst(SShell *sha, SShell *shb, SShell *into, SSurface::CombineAs type);
     void MakeIntersectionCurvesAgainst(SShell *against, SShell *into);
     void MakeClassifyingBsps(SShell *useCurvesFrom);
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index 0dafd42db..5e0b490fd 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -64,6 +64,7 @@ set(testsuite_SOURCES
     request/ttf_text/test.cpp
     request/workplane/test.cpp
     group/boolean_coplanar_union/test.cpp
+    group/boolean_cross_vertex/test.cpp
     group/boolean_knife_edge/test.cpp
     group/boolean_tangent_edge/test.cpp
     group/boolean_tangent_fillet/test.cpp
diff --git a/test/group/boolean_cross_vertex/normal.slvs b/test/group/boolean_cross_vertex/normal.slvs
new file mode 100644
index 000000000..053297958
--- /dev/null
+++ b/test/group/boolean_cross_vertex/normal.slvs
@@ -0,0 +1,2130 @@
+±²³SolveSpaceREVa
+
+
+Group.h.v=00000001
+Group.type=5000
+Group.name=#references
+Group.color=ff000000
+Group.skipFirst=0
+Group.predef.swapUV=0
+Group.predef.negateU=0
+Group.predef.negateV=0
+Group.visible=1
+Group.suppress=0
+Group.relaxConstraints=0
+Group.allowRedundant=0
+Group.allDimsReference=0
+Group.scale=1.00000000000000000000
+Group.remap={
+}
+AddGroup
+
+Group.h.v=00000002
+Group.type=5001
+Group.order=1
+Group.name=sketch-square
+Group.activeWorkplane.v=80020000
+Group.color=ff000000
+Group.subtype=6000
+Group.skipFirst=0
+Group.predef.q.w=1.00000000000000000000
+Group.predef.origin.v=00010001
+Group.predef.swapUV=0
+Group.predef.negateU=0
+Group.predef.negateV=0
+Group.visible=1
+Group.suppress=0
+Group.relaxConstraints=0
+Group.allowRedundant=0
+Group.allDimsReference=0
+Group.scale=1.00000000000000000000
+Group.remap={
+}
+AddGroup
+
+Group.h.v=00000003
+Group.type=5100
+Group.order=2
+Group.name=extrude-cube
+Group.opA.v=00000002
+Group.color=00646464
+Group.subtype=7001
+Group.skipFirst=0
+Group.predef.entityB.v=80020000
+Group.predef.swapUV=0
+Group.predef.negateU=0
+Group.predef.negateV=0
+Group.visible=1
+Group.suppress=0
+Group.relaxConstraints=0
+Group.allowRedundant=0
+Group.allDimsReference=0
+Group.scale=1.00000000000000000000
+Group.remap={
+    1 00040000 1002
+    2 00040001 1002
+    3 00040002 1002
+    4 00040000 1001
+    5 00040001 1001
+    6 00040002 1001
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+    40 80020002 1002
+    41 80020001 1001
+    42 80020002 1001
+    43 80020002 1003
+    44 00000000 1001
+    45 00000000 1002
+}
+AddGroup
+
+Group.h.v=00000004
+Group.type=5001
+Group.order=3
+Group.name=sketch-fillet
+Group.activeWorkplane.v=80040000
+Group.color=00646464
+Group.subtype=6001
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+Group.predef.origin.v=80030018
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+Group.predef.entityC.v=80030016
+Group.predef.swapUV=0
+Group.predef.negateU=1
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+Group.visible=1
+Group.suppress=0
+Group.relaxConstraints=0
+Group.allowRedundant=0
+Group.allDimsReference=0
+Group.scale=1.00000000000000000000
+Group.remap={
+}
+AddGroup
+
+Group.h.v=00000005
+Group.type=5100
+Group.order=4
+Group.name=cut
+Group.opA.v=00000004
+Group.color=00646464
+Group.subtype=7001
+Group.skipFirst=0
+Group.meshCombine=1
+Group.predef.entityB.v=80040000
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+Group.suppress=0
+Group.relaxConstraints=0
+Group.allowRedundant=0
+Group.allDimsReference=0
+Group.scale=1.00000000000000000000
+Group.remap={
+    1 00080000 1002
+    2 00080001 1002
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+    4 00080000 1001
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+    6 00080002 1001
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+    36 80040002 1002
+    37 80040001 1001
+    38 80040002 1001
+    39 80040002 1003
+    40 00000000 1001
+    41 00000000 1002
+}
+AddGroup
+
+Param.h.v.=00010010
+AddParam
+
+Param.h.v.=00010011
+AddParam
+
+Param.h.v.=00010012
+AddParam
+
+Param.h.v.=00010020
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+AddParam
+
+Param.h.v.=00010021
+AddParam
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+Param.h.v.=00010022
+AddParam
+
+Param.h.v.=00010023
+AddParam
+
+Param.h.v.=00020010
+AddParam
+
+Param.h.v.=00020011
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+Param.h.v.=00020012
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+Param.h.v.=00020020
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+Request.h.v=00000001
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+Request.h.v=00000002
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+Request.h.v=00000004
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+Entity.actVisible=1
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+Entity.h.v=00040002
+Entity.type=2001
+Entity.construction=0
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+Entity.actVisible=1
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+Entity.h.v=00050000
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+Entity.construction=0
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+Entity.actPoint.x=-30.00000000000000000000
+Entity.actPoint.y=-30.00000000000000000000
+Entity.actVisible=1
+AddEntity
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+Entity.h.v=00050002
+Entity.type=2001
+Entity.construction=0
+Entity.workplane.v=80020000
+Entity.actPoint.x=30.00000000000000000000
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+Entity.actVisible=1
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+Entity.h.v=00060000
+Entity.type=11000
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+Entity.actVisible=1
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+Entity.h.v=00060001
+Entity.type=2001
+Entity.construction=0
+Entity.workplane.v=80020000
+Entity.actPoint.x=-30.00000000000000000000
+Entity.actPoint.y=30.00000000000000000000
+Entity.actVisible=1
+AddEntity
+
+Entity.h.v=00060002
+Entity.type=2001
+Entity.construction=0
+Entity.workplane.v=80020000
+Entity.actPoint.x=-30.00000000000000000000
+Entity.actPoint.y=-30.00000000000000000000
+Entity.actVisible=1
+AddEntity
+
+Entity.h.v=00070000
+Entity.type=11000
+Entity.construction=0
+Entity.point[0].v=00070001
+Entity.point[1].v=00070002
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+Entity.actVisible=1
+AddEntity
+
+Entity.h.v=00070001
+Entity.type=2001
+Entity.construction=0
+Entity.workplane.v=80020000
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diff --git a/test/group/boolean_cross_vertex/test.cpp b/test/group/boolean_cross_vertex/test.cpp
new file mode 100644
index 000000000..7d38ee6f6
--- /dev/null
+++ b/test/group/boolean_cross_vertex/test.cpp
@@ -0,0 +1,37 @@
+#include "solvespace.h"
+
+#include "harness.h"
+
+// A cube minus a tool swept along a spline profile. The profile is tangent to
+// one face of the cube, and the tool's flat cap face is coincident with that
+// same face of the cube, so the tool's tangent edge runs within the cube's
+// face and crosses the cube's own edge there. That crossing point is a vertex
+// of neither input shell, and neither curve passes through a surface of the
+// other shell transversally at it, so SCurve::MakeCopySplitAgainst() splits
+// only the tool's edge (which does cross the cube's face) and leaves the
+// cube's edge whole. The cube's face is then trimmed by an edge whose two
+// halves classify differently, its trim polygon fails to assemble, and two
+// faces of the result go missing (issue #1743; the model is phkahler's
+// cube_cut_2).
+TEST_CASE(normal_watertight_volume) {
+    CHECK_LOAD("normal.slvs");
+
+    Group *g = SK.GetGroup(SS.GW.activeGroup);
+    g->GenerateDisplayItems();
+    SMesh *m = &g->displayMesh;
+    CHECK_FALSE(m->l.IsEmpty());
+
+    SEdgeList el = {};
+    bool inters, leaks;
+    SKdNode::From(m)->MakeCertainEdgesInto(&el,
+        EdgeKind::NAKED_OR_SELF_INTER, /*coplanarIsInter=*/true, &inters, &leaks);
+    CHECK_FALSE(inters);
+    CHECK_FALSE(leaks);
+    CHECK_TRUE(el.l.IsEmpty());
+    el.Clear();
+
+    // The same value that the mesh Boolean gives for this model (build it
+    // with Group.forceToMesh set), to twelve significant figures.
+    CHECK_EQ_EPS(m->CalculateVolume() / 203485.2242132, 1.0);
+}
+