Scutoid

Author

Eric W. Weisstein
August 31, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/SolidGeometry/Scutoid.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/Scutoid.html.

©2026 Wolfram Research, Inc.

Figure

A schematic scutoid with pentagonal and hexagonal ends and an intervening vertex.

With[
	{
		b = (Append[1.15 {Cos[#], Sin[#]}, 0] & ) /@ Table[Pi/2 + 2 Pi j/6, {j, 0, 5}],
		t = (Append[0.9 {Cos[#], Sin[#]}, 2] & ) /@ Table[Pi/2 + 2 Pi j/5, {j, 0, 4}],
		m = {0, -1.35, 1.05},
		ink = LightDarkSwitched[RGBColor[0.217, 0.217, 0.217], RGBColor[0.867, 0.867, 0.867]],
		fill1 = LightDarkSwitched[RGBColor[0.8, 0.87, 0.98], RGBColor[0.25, 0.38, 0.62]],
		fill2 = LightDarkSwitched[RGBColor[0.98, 0.84, 0.66], RGBColor[0.68, 0.36, 0.2]]
	},
	Graphics3D[
		{
			EdgeForm[Directive[ink, AbsoluteThickness[1.5]]],
			FaceForm[fill1],
			Polygon[t],
			Polygon[Reverse[b]],
			Polygon /@ {
				{t[[1]], t[[2]], b[[2]], b[[1]]},
				{t[[2]], t[[3]], b[[3]], b[[2]]},
				{t[[3]], m, b[[3]]},
				{t[[3]], t[[4]], b[[4]], m},
				{t[[4]], t[[5]], b[[5]], b[[4]]},
				{t[[5]], t[[1]], b[[6]], b[[5]]},
				{t[[1]], b[[1]], b[[6]]}
			},
			FaceForm[fill2],
			Polygon[{m, b[[4]], b[[3]]}]
		},
		Boxed -> False,
		Method -> {"ShrinkWrap" -> True}
	]
]