What kind of polyhedron is this?
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What kind of polyhedron is this? I understand 20 faces is the largest regular polyhedron, but this one seems to have 36 faces.
Source: It is the logo of the Green Climate Fund
geometry polyhedra
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quid♦
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up vote
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What kind of polyhedron is this? I understand 20 faces is the largest regular polyhedron, but this one seems to have 36 faces.
Source: It is the logo of the Green Climate Fund
geometry polyhedra
edited yesterday
quid♦
36.6k95092
asked yesterday
user616001
162
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user616001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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You count 36 visible faces, but it amounts to approximately twice (72) if you include the hidden faces.
– Jean Marie
yesterday
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
What kind of polyhedron is this? I understand 20 faces is the largest regular polyhedron, but this one seems to have 36 faces.
Source: It is the logo of the Green Climate Fund
geometry polyhedra
edited yesterday
quid♦
36.6k95092
asked yesterday
user616001
162
New contributor
user616001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
What kind of polyhedron is this? I understand 20 faces is the largest regular polyhedron, but this one seems to have 36 faces.
Source: It is the logo of the Green Climate Fund
geometry polyhedra
geometry polyhedra
edited yesterday
quid♦
36.6k95092
asked yesterday
user616001
162
New contributor
user616001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
quid♦
36.6k95092
asked yesterday
user616001
162
New contributor
user616001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
quid♦
36.6k95092
edited yesterday
quid♦
36.6k95092
edited yesterday
quid♦
36.6k95092
36.6k95092
asked yesterday
user616001
162
New contributor
user616001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
user616001
162
asked yesterday
user616001
162
162
New contributor
user616001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user616001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user616001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
You count 36 visible faces, but it amounts to approximately twice (72) if you include the hidden faces.
– Jean Marie
yesterday
add a comment |
You count 36 visible faces, but it amounts to approximately twice (72) if you include the hidden faces.
– Jean Marie
yesterday
You count 36 visible faces, but it amounts to approximately twice (72) if you include the hidden faces.
– Jean Marie
yesterday
You count 36 visible faces, but it amounts to approximately twice (72) if you include the hidden faces.
– Jean Marie
yesterday
add a comment |
1 Answer
1
active
oldest
votes
up vote
2
down vote
(Incorrect) I think it is a Pentakis dodecahedron with $60$ faces, $90$ edges and $32$ vertices.
Here is the rotating model.
Edit: It is actually a Pentakis icosidodecahedron with $80$ triangles
($20$ equilateral; $60$ isosceles), $120$ edges and $42$ vertices. (See the comments below)
answered yesterday
Tianlalu
2,315632
Thank you very much for a quick answer! Faces looked like perfect triangles, but I guess they are actually isosceles triangle, therefore it is not considered as a regular polyhedron?
– user616001
yesterday
A pentakis dodecahedron would have each pentagonal pyramid adjacent to five pentagonal pyramids, but that is not the case for the logo in question. I believe it's a pentakis icosidodecahedron, i.e. an icosidodecahedron with a pyramid on top of each pentagon.
– Rahul
yesterday
@Rahul : I think you are right. Should I delete my answer or just edit it in this case?
– Tianlalu
yesterday
Thank you Rahul and Tianlalu! In the corresponding wikipedia page en.wikipedia.org/wiki/Pentakis_icosidodecahedron , it says "It can also be topologically constructed from the icosahedron, dividing each triangular face into 4 triangles by adding mid-edge vertices. From this construction, all 80 triangles will be equilateral, but faces will be coplanar." Are you able to tell from the logo picture, if it is coplanar or not?
– user616001
yesterday
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
(Incorrect) I think it is a Pentakis dodecahedron with $60$ faces, $90$ edges and $32$ vertices.
Here is the rotating model.
Edit: It is actually a Pentakis icosidodecahedron with $80$ triangles
($20$ equilateral; $60$ isosceles), $120$ edges and $42$ vertices. (See the comments below)
answered yesterday
Tianlalu
2,315632
Thank you very much for a quick answer! Faces looked like perfect triangles, but I guess they are actually isosceles triangle, therefore it is not considered as a regular polyhedron?
– user616001
yesterday
A pentakis dodecahedron would have each pentagonal pyramid adjacent to five pentagonal pyramids, but that is not the case for the logo in question. I believe it's a pentakis icosidodecahedron, i.e. an icosidodecahedron with a pyramid on top of each pentagon.
– Rahul
yesterday
@Rahul : I think you are right. Should I delete my answer or just edit it in this case?
– Tianlalu
yesterday
Thank you Rahul and Tianlalu! In the corresponding wikipedia page en.wikipedia.org/wiki/Pentakis_icosidodecahedron , it says "It can also be topologically constructed from the icosahedron, dividing each triangular face into 4 triangles by adding mid-edge vertices. From this construction, all 80 triangles will be equilateral, but faces will be coplanar." Are you able to tell from the logo picture, if it is coplanar or not?
– user616001
yesterday
add a comment |
up vote
2
down vote
(Incorrect) I think it is a Pentakis dodecahedron with $60$ faces, $90$ edges and $32$ vertices.
Here is the rotating model.
Edit: It is actually a Pentakis icosidodecahedron with $80$ triangles
($20$ equilateral; $60$ isosceles), $120$ edges and $42$ vertices. (See the comments below)
answered yesterday
Tianlalu
2,315632
Thank you very much for a quick answer! Faces looked like perfect triangles, but I guess they are actually isosceles triangle, therefore it is not considered as a regular polyhedron?
– user616001
yesterday
A pentakis dodecahedron would have each pentagonal pyramid adjacent to five pentagonal pyramids, but that is not the case for the logo in question. I believe it's a pentakis icosidodecahedron, i.e. an icosidodecahedron with a pyramid on top of each pentagon.
– Rahul
yesterday
@Rahul : I think you are right. Should I delete my answer or just edit it in this case?
– Tianlalu
yesterday
Thank you Rahul and Tianlalu! In the corresponding wikipedia page en.wikipedia.org/wiki/Pentakis_icosidodecahedron , it says "It can also be topologically constructed from the icosahedron, dividing each triangular face into 4 triangles by adding mid-edge vertices. From this construction, all 80 triangles will be equilateral, but faces will be coplanar." Are you able to tell from the logo picture, if it is coplanar or not?
– user616001
yesterday
add a comment |
up vote
2
down vote
up vote
2
down vote
(Incorrect) I think it is a Pentakis dodecahedron with $60$ faces, $90$ edges and $32$ vertices.
Here is the rotating model.
Edit: It is actually a Pentakis icosidodecahedron with $80$ triangles
($20$ equilateral; $60$ isosceles), $120$ edges and $42$ vertices. (See the comments below)
answered yesterday
Tianlalu
2,315632
(Incorrect) I think it is a Pentakis dodecahedron with $60$ faces, $90$ edges and $32$ vertices.
Here is the rotating model.
Edit: It is actually a Pentakis icosidodecahedron with $80$ triangles
($20$ equilateral; $60$ isosceles), $120$ edges and $42$ vertices. (See the comments below)
answered yesterday
Tianlalu
2,315632
edited yesterday
answered yesterday
Tianlalu
2,315632
answered yesterday
Tianlalu
2,315632
answered yesterday
Tianlalu
2,315632
2,315632
Thank you very much for a quick answer! Faces looked like perfect triangles, but I guess they are actually isosceles triangle, therefore it is not considered as a regular polyhedron?
– user616001
yesterday
A pentakis dodecahedron would have each pentagonal pyramid adjacent to five pentagonal pyramids, but that is not the case for the logo in question. I believe it's a pentakis icosidodecahedron, i.e. an icosidodecahedron with a pyramid on top of each pentagon.
– Rahul
yesterday
@Rahul : I think you are right. Should I delete my answer or just edit it in this case?
– Tianlalu
yesterday
Thank you Rahul and Tianlalu! In the corresponding wikipedia page en.wikipedia.org/wiki/Pentakis_icosidodecahedron , it says "It can also be topologically constructed from the icosahedron, dividing each triangular face into 4 triangles by adding mid-edge vertices. From this construction, all 80 triangles will be equilateral, but faces will be coplanar." Are you able to tell from the logo picture, if it is coplanar or not?
– user616001
yesterday
add a comment |
Thank you very much for a quick answer! Faces looked like perfect triangles, but I guess they are actually isosceles triangle, therefore it is not considered as a regular polyhedron?
– user616001
yesterday
A pentakis dodecahedron would have each pentagonal pyramid adjacent to five pentagonal pyramids, but that is not the case for the logo in question. I believe it's a pentakis icosidodecahedron, i.e. an icosidodecahedron with a pyramid on top of each pentagon.
– Rahul
yesterday
@Rahul : I think you are right. Should I delete my answer or just edit it in this case?
– Tianlalu
yesterday
Thank you Rahul and Tianlalu! In the corresponding wikipedia page en.wikipedia.org/wiki/Pentakis_icosidodecahedron , it says "It can also be topologically constructed from the icosahedron, dividing each triangular face into 4 triangles by adding mid-edge vertices. From this construction, all 80 triangles will be equilateral, but faces will be coplanar." Are you able to tell from the logo picture, if it is coplanar or not?
– user616001
yesterday
Thank you very much for a quick answer! Faces looked like perfect triangles, but I guess they are actually isosceles triangle, therefore it is not considered as a regular polyhedron?
– user616001
yesterday
Thank you very much for a quick answer! Faces looked like perfect triangles, but I guess they are actually isosceles triangle, therefore it is not considered as a regular polyhedron?
– user616001
yesterday
A pentakis dodecahedron would have each pentagonal pyramid adjacent to five pentagonal pyramids, but that is not the case for the logo in question. I believe it's a pentakis icosidodecahedron, i.e. an icosidodecahedron with a pyramid on top of each pentagon.
– Rahul
yesterday
A pentakis dodecahedron would have each pentagonal pyramid adjacent to five pentagonal pyramids, but that is not the case for the logo in question. I believe it's a pentakis icosidodecahedron, i.e. an icosidodecahedron with a pyramid on top of each pentagon.
– Rahul
yesterday
@Rahul : I think you are right. Should I delete my answer or just edit it in this case?
– Tianlalu
yesterday
@Rahul : I think you are right. Should I delete my answer or just edit it in this case?
– Tianlalu
yesterday
Thank you Rahul and Tianlalu! In the corresponding wikipedia page en.wikipedia.org/wiki/Pentakis_icosidodecahedron , it says "It can also be topologically constructed from the icosahedron, dividing each triangular face into 4 triangles by adding mid-edge vertices. From this construction, all 80 triangles will be equilateral, but faces will be coplanar." Are you able to tell from the logo picture, if it is coplanar or not?
– user616001
yesterday
Thank you Rahul and Tianlalu! In the corresponding wikipedia page en.wikipedia.org/wiki/Pentakis_icosidodecahedron , it says "It can also be topologically constructed from the icosahedron, dividing each triangular face into 4 triangles by adding mid-edge vertices. From this construction, all 80 triangles will be equilateral, but faces will be coplanar." Are you able to tell from the logo picture, if it is coplanar or not?
– user616001
yesterday
add a comment |
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You count 36 visible faces, but it amounts to approximately twice (72) if you include the hidden faces.
– Jean Marie
yesterday