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Kepler-Poinsot Polyhedron

Members

great dodecahedron | great icosahedron | great stellated dodecahedron | small stellated dodecahedron

Visual representations

Visual representations

Combinatorial properties

 | vertices | edges | faces
great dodecahedron | 12 | 30 | 12 (12 pentagons)
great icosahedron | 12 | 30 | 20 (20 triangles)
great stellated dodecahedron | 20 | 30 | 12 (12 pentagrams)
small stellated dodecahedron | 12 | 30 | 12 (12 pentagrams)

Edge lengths

1 (30 edges)

1 (30 edges)

1 (30 edges)

1 (30 edges)

Geometric properties

 | surface area
great dodecahedron | 3 sqrt(5 (5 + 2 sqrt(5)))
great icosahedron | 5 sqrt(3)
great stellated dodecahedron | 15 sqrt(85 - 38 sqrt(5))
small stellated dodecahedron | 15 sqrt(85 - 38 sqrt(5))
 | circumradius
great dodecahedron | sqrt(5/8 + sqrt(5)/8)
great icosahedron | root of 16 x^4 - 20 x^2 + 5 near x = 0.587785
great stellated dodecahedron | sqrt(3)/(2 ϕ)
small stellated dodecahedron | 5^(1/4)/(2 sqrt(ϕ))
 | midradius
great dodecahedron | ϕ/2
great icosahedron | 1/(2 ϕ)
great stellated dodecahedron | 1 - ϕ/2
small stellated dodecahedron | 1/2 sqrt(1/2 (3 - sqrt(5)))
 | inradius
great stellated dodecahedron | 1/2 sqrt(1/10 (25 - 11 sqrt(5)))
small stellated dodecahedron | root of 80 x^4 - 20 x^2 + 1 near x = 0.262866
(assuming unit edge lengths)

Skeleton graphs

 | skeleton graph name
great dodecahedron | icosahedral graph
great icosahedron | icosahedral graph
great stellated dodecahedron | dodecahedral graph
small stellated dodecahedron | icosahedral graph

Dual polyhedra

 | dual name
great dodecahedron | small stellated dodecahedron
great icosahedron | great stellated dodecahedron
great stellated dodecahedron | great icosahedron
small stellated dodecahedron | great dodecahedron

Dual skeleton graphs

 | dual skeleton name
great dodecahedron | icosahedral graph
great icosahedron | dodecahedral graph
great stellated dodecahedron | icosahedral graph
small stellated dodecahedron | icosahedral graph

Common properties

amphichiral | concave | equilateral | Kepler-Poinsot | rigid | uniform | uniform dual

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What Is Domain In Math

What Is Domain In Math ‘

What Is Domain In Math

What Is Domain In Math ‘

Volume of a Sphere

Volume of a Sphere ‘

Area of a Triangle

Area of a Triangle ‘

Distance Formula

Distance Formula ‘

Distance Formula

Distance Formula ‘

Volume of a Cylinder

Volume of a Cylinder ‘

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