Convex triamond polyhedron

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The convex triamond polyhedron triamond pentagonal rotunda 2 + triamond pentagonal bicupola. Its triamond faces are colored in red.

A convex triamond polyhedron is a strictly convex polyhedron with all regular faces of edge length 1 except for at least one "triamond", defined as a trapezoid with edge lengths 2-1-1-1 (a blend of three coplanar equilateral triangles).[1] In such polyhedra, triamonds always come in pairs joined at their length-2 edges. There are 40 known convex triamond polyhedra, found by Roger Kaufman and others. All are achiral. It is not known if there are others.

List of convex triamond polyhedra[edit | edit source]

The following are all of the convex triamond polyhedra that are currently known.[1] The categories are those given by Roger Kaufman.

List of convex triamond polyhedra
Name Image Element counts Discoverer Category
Vertices Edges Faces Triamond faces
Triamond stretched octahedron 8 14 8 4 Roger Kaufman Stretched platonics
Triamond stretched icosahedron 16 36 22 4 Alex Doskey Stretched platonics
Triamond triangular bifrustum 9 15 8 6 Roger Kaufman Bifrusta
Triamond square bifrustum 12 20 10 8 Roger Kaufman Bifrusta
Triamond pentagonal bifrustum 15 25 12 10 Robert Austin Bifrusta
Triamond triangular bicupola 18 30 14 6 Roger Kaufman Bicupolae
Triamond square bicupola 24 40 18 8 Roger Kaufman Bicupolae
Triamond pentagonal bicupola 30 50 22 10 Roger Kaufman Bicupolae
Triamond bilateral cupola + stretched J1 wedge 10 17 9 4 Roger Kaufman Triamond bilateral cupola augmentations
Triamond bilateral cupola + stretched J1 wedge + meta J1 11 21 12 4 Jim McNeil Triamond bilateral cupola augmentations
Triamond bilateral cupola + stretched J1 wedge + para J1 11 21 12 4 Roger Kaufman Triamond bilateral cupola augmentations
Triamond bilateral cupola + stretched J1 wedge + 2 J1 12 25 15 4 Roger Kaufman Triamond bilateral cupola augmentations
Triamond pentagonal birotunda 50 80 32 10 Jim McNeil Rotunda augmentations
Triamond pentagonal rotunda 1 + triamond pentagonal cupola 40 65 27 10 Jim McNeil Rotunda augmentations
Triamond pentagonal rotunda 2 + triamond pentagonal cupola 50 80 32 10 Jim McNeil Rotunda augmentations
Triamond gyroelongated square bicupola 32 56 26 16 Roger Kaufman Augmentations of triamond antiprisms, order 1
Triamond gyroelongated pentagonal bicupola 40 70 32 20 Roger Kaufman Augmentations of triamond antiprisms, order 1
Triamond antiprism 2,2 6 9 5 2 Roger Kaufman Augmentations of the triamond antiprism 2,2
Triamond antiprism 2,2 + triamond antiprism 2,2 8 14 8 2 Roger Kaufman Augmentations of the triamond antiprism 2,2
Triamond antiprism 4,2 + triamond square frustrum 16 28 14 8 Roger Kaufman Augmentations of the triamond antiprism 4,2
Triamond antiprism 4,2 + triamond square frustrum + ortho J4 20 40 22 8 Roger Kaufman Augmentations of the triamond antiprism 4,2
Triamond antiprism 4,2 + triamond square frustrum + gyro J4 20 40 22 8 Roger Kaufman Augmentations of the triamond antiprism 4,2
Triamond antiprism 5,2 + triamond pentagonal cupola 20 35 17 10 Roger Kaufman Augmentations of the triamond antiprism 5,2
Triamond antiprism 5,2 + triamond pentagonal cupola + gyro J5 25 50 27 10 Roger Kaufman Augmentations of the triamond antiprism 5,2
Triamond antiprism 5,2 + triamond pentagonal cupola + ortho J5 25 50 27 10 Roger Kaufman Augmentations of the triamond antiprism 5,2
Triamond antiprism 5,2 + triamond pentagonal cupola + J6 30 60 32 10 Roger Kaufman Augmentations of the triamond antiprism 5,2
Triamond stretched J13 10 20 12 2 Roger Kaufman Stretched Johnson solids
Triamond stretched J17 14 30 18 4 Jim McNeil Stretched Johnson solids
Triamond stretched J84 12 25 15 2 Jim McNeil Stretched Johnson solids
Triamond stretched J86 14 29 17 2 Jim McNeil Stretched Johnson solids
Triamond stretched J88 18 39 23 2 Jim McNeil Stretched Johnson solids
Triamond stretched J51 12 24 14 6 Jim McNeil Stretched Johnson solids
Triamond J91 + 2 J2 15 31 18 2 Roger Kaufman J91 augmentations
Triamond J91 + 4 J2 - J2 15 31 18 4 Roger Kaufman J91 augmentations
Triamond J91 + 4 J2 - 2 J2 (cis) 14 26 14 4 Roger Kaufman J91 augmentations
Triamond J91 + 4 J2 - 2 J2 (trans) 14 26 14 4 Roger Kaufman J91 augmentations
Triamond J3 section 7 11 6 2 Roger Kaufman Sectioned Johnson solids
Triamond J92 section +
triamond J92 section		 16 32 18 2 Roger Kaufman Sectioned Johnson solids
Triamond J92 section + stretched J2 wedge 13 26 15 2 Roger Kaufman Sectioned Johnson solids
Misc1 10 22 14 2 Roger Kaufman Miscellaneous

References[edit | edit source]

  1. ↑ 1.0 1.1 Kaufman, Roger. "Convex Triamond Regular Polyhedra."
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