diff --git a/tests/kernel-cases/surfaces/cov-unstitch-box-every-face/expected.json b/tests/kernel-cases/surfaces/cov-unstitch-box-every-face/expected.json
new file mode 100644
index 0000000000..0be8573b4f
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-unstitch-box-every-face/expected.json
@@ -0,0 +1,26 @@
+{
+ "sources": [],
+ "what": "a 20 x 10 x 10 box unstitched: six surface bodies, one a face",
+ "source": "analytic",
+ "method": "no faces picked: every face its own surface body; areas 2 (200 + 200 + 100) = 1000; each face keeps its 4 edges, now free: 24",
+ "valid": false,
+ "body_count": 6,
+ "faces": 6,
+ "boundary_edges": 24,
+ "area_mm2": 1000.0,
+ "surface_types": [
+  "plane"
+ ],
+ "bbox": {
+  "min": [
+   0,
+   0,
+   0
+  ],
+  "max": [
+   20,
+   10,
+   10
+  ]
+ }
+}
diff --git a/tests/kernel-cases/surfaces/cov-unstitch-box-every-face/recipe.json b/tests/kernel-cases/surfaces/cov-unstitch-box-every-face/recipe.json
new file mode 100644
index 0000000000..8bfecc18bf
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-unstitch-box-every-face/recipe.json
@@ -0,0 +1,19 @@
+{
+ "commands": [
+  {
+   "command": "solid.box",
+   "params": {
+    "length": 20,
+    "width": 10,
+    "height": 10,
+    "body_name": "Box"
+   }
+  },
+  {
+   "command": "surface.unstitch",
+   "params": {
+    "body": "Box"
+   }
+  }
+ ]
+}
diff --git a/tests/kernel-cases/surfaces/cov-unstitch-box-top-only/expected.json b/tests/kernel-cases/surfaces/cov-unstitch-box-top-only/expected.json
new file mode 100644
index 0000000000..e0ce57bb9a
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-unstitch-box-top-only/expected.json
@@ -0,0 +1,14 @@
+{
+ "sources": [],
+ "what": "the top of a box unstitched: the top a surface body, the open box the other",
+ "source": "analytic",
+ "method": "the picked face (top, 200) its own body, the other five (800) stay together under the box's name: 2 bodies, area 1000, free edges 4 (the top's) + 4 (the open box's rim)",
+ "valid": false,
+ "body_count": 2,
+ "faces": 6,
+ "boundary_edges": 8,
+ "area_mm2": 1000.0,
+ "surface_types": [
+  "plane"
+ ]
+}
diff --git a/tests/kernel-cases/surfaces/cov-unstitch-box-top-only/recipe.json b/tests/kernel-cases/surfaces/cov-unstitch-box-top-only/recipe.json
new file mode 100644
index 0000000000..33bf21733f
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-unstitch-box-top-only/recipe.json
@@ -0,0 +1,27 @@
+{
+ "commands": [
+  {
+   "command": "solid.box",
+   "params": {
+    "length": 20,
+    "width": 10,
+    "height": 10,
+    "body_name": "Box"
+   }
+  },
+  {
+   "command": "surface.unstitch",
+   "params": {
+    "body": "Box",
+    "faces": [
+     [
+      10,
+      5,
+      10
+     ]
+    ],
+    "body_name": "Top"
+   }
+  }
+ ]
+}
diff --git a/tests/kernel-cases/surfaces/cov-unstitch-cylinder-caps-and-side/expected.json b/tests/kernel-cases/surfaces/cov-unstitch-cylinder-caps-and-side/expected.json
new file mode 100644
index 0000000000..5781d8cc97
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-unstitch-cylinder-caps-and-side/expected.json
@@ -0,0 +1,15 @@
+{
+ "sources": [],
+ "what": "a cylinder r 5, 10 high, unstitched: the side and the two caps, each a surface body",
+ "source": "analytic",
+ "method": "side 2 pi 5 10 = 314.16 (a cylinder, closed on its seam), caps 2 x 25 pi = 157.08 (planes): 3 bodies, area 471.24; free edges: each cap's circle and the side's two circles, 4",
+ "valid": false,
+ "body_count": 3,
+ "faces": 3,
+ "boundary_edges": 4,
+ "area_mm2": 471.23889803846896,
+ "surface_types": [
+  "cylinder",
+  "plane"
+ ]
+}
diff --git a/tests/kernel-cases/surfaces/cov-unstitch-cylinder-caps-and-side/recipe.json b/tests/kernel-cases/surfaces/cov-unstitch-cylinder-caps-and-side/recipe.json
new file mode 100644
index 0000000000..b78647a632
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-unstitch-cylinder-caps-and-side/recipe.json
@@ -0,0 +1,18 @@
+{
+ "commands": [
+  {
+   "command": "solid.cylinder",
+   "params": {
+    "radius": 5,
+    "height": 10,
+    "body_name": "Post"
+   }
+  },
+  {
+   "command": "surface.unstitch",
+   "params": {
+    "body": "Post"
+   }
+  }
+ ]
+}
diff --git a/tests/kernel-cases/surfaces/cov-unstitch-one-face-sheet-refused/expected.json b/tests/kernel-cases/surfaces/cov-unstitch-one-face-sheet-refused/expected.json
new file mode 100644
index 0000000000..6ab0afc1aa
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-unstitch-one-face-sheet-refused/expected.json
@@ -0,0 +1,8 @@
+{
+ "sources": [],
+ "what": "unstitch on a body of one face: nothing to take apart, refused",
+ "source": "invariants",
+ "method": "a single face is already as far apart as it goes",
+ "outcome": "refused",
+ "refusal": "the body has one face: nothing to unstitch"
+}
diff --git a/tests/kernel-cases/surfaces/cov-unstitch-one-face-sheet-refused/recipe.json b/tests/kernel-cases/surfaces/cov-unstitch-one-face-sheet-refused/recipe.json
new file mode 100644
index 0000000000..ac3b9012f2
--- /dev/null
+++ b/tests/kernel-cases/surfaces/cov-unstitch-one-face-sheet-refused/recipe.json
@@ -0,0 +1,57 @@
+{
+ "commands": [
+  {
+   "command": "sketch.create",
+   "params": {
+    "plane": {
+     "origin": [
+      0,
+      0,
+      0
+     ],
+     "x_dir": [
+      1,
+      0,
+      0
+     ],
+     "y_dir": [
+      0,
+      1,
+      0
+     ]
+    },
+    "name": "Sheet sketch"
+   }
+  },
+  {
+   "command": "sketch.rectangle.two_point",
+   "params": {
+    "p0": [
+     0,
+     0
+    ],
+    "p1": [
+     10,
+     10
+    ]
+   }
+  },
+  {
+   "command": "sketch.finish",
+   "params": {}
+  },
+  {
+   "command": "surface.patch",
+   "params": {
+    "sketch": "Sheet sketch",
+    "body_name": "Sheet"
+   }
+  },
+  {
+   "command": "surface.unstitch",
+   "params": {
+    "body": "Sheet"
+   }
+  }
+ ]
+}