Count the corners, edges and faces of a cut cube

Clash Royale CLAN TAG#URR8PPP

up vote
7
down vote

favorite

Coming from this sandbox post

This is inspired from an 8th graders math test

Intro

We have a cube with following corners

A(0, 0, 0)
B(1, 0, 0)
C(1, 1, 0)
D(0, 1, 0)
E(0, 0, 1)
F(1, 0, 1)
G(1, 1, 1)
H(0, 1, 1)

This cube clearly has 8 corners, 12 edges and 6 faces. If we now cut off corner G, such that our cut plane goes exactly through the middle of each adjacent original edge, we add 2 new corners, 3 new edges and one new face. Please enjoy this hand drawn piece of art, for better clarification

Input

Given a list of corners (in this example identified by A-H), that will be cut off, compute the new number of corners, edges and faces.

You make take the input in any form you like, as long as it responds to the same corners (e.g. instead of A-H you can use 1-8 or 0-7, you can assume it to be a list, csv, whatever)

You can assume the list to be distinct (every corner will appear once at most), but it may be empty. The list will never contain non existing corners.

Output

Output three numbers corresponding to the number of corners, edges and faces. Output as a list is explicitly allowed.
Trailing whitespaces are allowed

Examples

 -> 8, 12, 6 (empty list) 
A -> 10, 15, 7 
A,C -> 12, 18, 8 
A,C,F -> 14, 21, 9 
A,B,C -> 12, 19, 9 
A,B,C,D -> 12, 20, 10 

Finally, this is codegolf, thus the shortest answer in bytes wins. Please refrain from standard loopholes.

code-golf

share|improve this question

edited 3 hours ago

asked 3 hours ago

infinitezero

21613

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  Interesting... So cutting off adjacent corners will mean they share one corner, and eliminate one edge? This is more complex than it seems at first
  – Jo King
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Since imgur being blocked in Turkey, I can not see the image. Can you please send an alternate image link
  – Windmill Cookies
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @JoKing yes that is correct.
  – infinitezero
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @WindmillCookies I'm sorry, I didn't know that. I've used a different host now.
  – infinitezero
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  For example, may I use 0 for A, 1 for C, 2 for B, 3 for D, 4 for E, 5 for G, 6 for F, 7 for H? Or should I keep the order of ABCDEFGH?
  – tsh
  2 hours ago
  
  

  
  
  
  

 | 
show 1 more comment

up vote
7
down vote

favorite

Coming from this sandbox post

This is inspired from an 8th graders math test

Intro

We have a cube with following corners

A(0, 0, 0)
B(1, 0, 0)
C(1, 1, 0)
D(0, 1, 0)
E(0, 0, 1)
F(1, 0, 1)
G(1, 1, 1)
H(0, 1, 1)

This cube clearly has 8 corners, 12 edges and 6 faces. If we now cut off corner G, such that our cut plane goes exactly through the middle of each adjacent original edge, we add 2 new corners, 3 new edges and one new face. Please enjoy this hand drawn piece of art, for better clarification

Input

Given a list of corners (in this example identified by A-H), that will be cut off, compute the new number of corners, edges and faces.

You make take the input in any form you like, as long as it responds to the same corners (e.g. instead of A-H you can use 1-8 or 0-7, you can assume it to be a list, csv, whatever)

You can assume the list to be distinct (every corner will appear once at most), but it may be empty. The list will never contain non existing corners.

Output

Output three numbers corresponding to the number of corners, edges and faces. Output as a list is explicitly allowed.
Trailing whitespaces are allowed

Examples

 -> 8, 12, 6 (empty list) 
A -> 10, 15, 7 
A,C -> 12, 18, 8 
A,C,F -> 14, 21, 9 
A,B,C -> 12, 19, 9 
A,B,C,D -> 12, 20, 10 

Finally, this is codegolf, thus the shortest answer in bytes wins. Please refrain from standard loopholes.

code-golf

share|improve this question

edited 3 hours ago

asked 3 hours ago

infinitezero

21613

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  Interesting... So cutting off adjacent corners will mean they share one corner, and eliminate one edge? This is more complex than it seems at first
  – Jo King
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Since imgur being blocked in Turkey, I can not see the image. Can you please send an alternate image link
  – Windmill Cookies
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @JoKing yes that is correct.
  – infinitezero
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @WindmillCookies I'm sorry, I didn't know that. I've used a different host now.
  – infinitezero
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  For example, may I use 0 for A, 1 for C, 2 for B, 3 for D, 4 for E, 5 for G, 6 for F, 7 for H? Or should I keep the order of ABCDEFGH?
  – tsh
  2 hours ago
  
  

  
  
  
  

 | 
show 1 more comment

up vote
7
down vote

favorite

up vote
7
down vote

favorite

Coming from this sandbox post

This is inspired from an 8th graders math test

Intro

We have a cube with following corners

A(0, 0, 0)
B(1, 0, 0)
C(1, 1, 0)
D(0, 1, 0)
E(0, 0, 1)
F(1, 0, 1)
G(1, 1, 1)
H(0, 1, 1)

This cube clearly has 8 corners, 12 edges and 6 faces. If we now cut off corner G, such that our cut plane goes exactly through the middle of each adjacent original edge, we add 2 new corners, 3 new edges and one new face. Please enjoy this hand drawn piece of art, for better clarification

Input

Given a list of corners (in this example identified by A-H), that will be cut off, compute the new number of corners, edges and faces.

You make take the input in any form you like, as long as it responds to the same corners (e.g. instead of A-H you can use 1-8 or 0-7, you can assume it to be a list, csv, whatever)

You can assume the list to be distinct (every corner will appear once at most), but it may be empty. The list will never contain non existing corners.

Output

Output three numbers corresponding to the number of corners, edges and faces. Output as a list is explicitly allowed.
Trailing whitespaces are allowed

Examples

 -> 8, 12, 6 (empty list) 
A -> 10, 15, 7 
A,C -> 12, 18, 8 
A,C,F -> 14, 21, 9 
A,B,C -> 12, 19, 9 
A,B,C,D -> 12, 20, 10 

Finally, this is codegolf, thus the shortest answer in bytes wins. Please refrain from standard loopholes.

code-golf

share|improve this question

edited 3 hours ago

asked 3 hours ago

infinitezero

21613

Coming from this sandbox post

This is inspired from an 8th graders math test

Intro

We have a cube with following corners

A(0, 0, 0)
B(1, 0, 0)
C(1, 1, 0)
D(0, 1, 0)
E(0, 0, 1)
F(1, 0, 1)
G(1, 1, 1)
H(0, 1, 1)

This cube clearly has 8 corners, 12 edges and 6 faces. If we now cut off corner G, such that our cut plane goes exactly through the middle of each adjacent original edge, we add 2 new corners, 3 new edges and one new face. Please enjoy this hand drawn piece of art, for better clarification

Input

Given a list of corners (in this example identified by A-H), that will be cut off, compute the new number of corners, edges and faces.

You make take the input in any form you like, as long as it responds to the same corners (e.g. instead of A-H you can use 1-8 or 0-7, you can assume it to be a list, csv, whatever)

You can assume the list to be distinct (every corner will appear once at most), but it may be empty. The list will never contain non existing corners.

Output

Output three numbers corresponding to the number of corners, edges and faces. Output as a list is explicitly allowed.
Trailing whitespaces are allowed

Examples

 -> 8, 12, 6 (empty list) 
A -> 10, 15, 7 
A,C -> 12, 18, 8 
A,C,F -> 14, 21, 9 
A,B,C -> 12, 19, 9 
A,B,C,D -> 12, 20, 10 

Finally, this is codegolf, thus the shortest answer in bytes wins. Please refrain from standard loopholes.

code-golf

code-golf

share|improve this question

edited 3 hours ago

asked 3 hours ago

infinitezero

21613

share|improve this question

edited 3 hours ago

asked 3 hours ago

infinitezero

21613

share|improve this question

share|improve this question

edited 3 hours ago

edited 3 hours ago

edited 3 hours ago

asked 3 hours ago

infinitezero

21613

asked 3 hours ago

infinitezero

21613

asked 3 hours ago

infinitezero

21613

21613

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  Interesting... So cutting off adjacent corners will mean they share one corner, and eliminate one edge? This is more complex than it seems at first
  – Jo King
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Since imgur being blocked in Turkey, I can not see the image. Can you please send an alternate image link
  – Windmill Cookies
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @JoKing yes that is correct.
  – infinitezero
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @WindmillCookies I'm sorry, I didn't know that. I've used a different host now.
  – infinitezero
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  For example, may I use 0 for A, 1 for C, 2 for B, 3 for D, 4 for E, 5 for G, 6 for F, 7 for H? Or should I keep the order of ABCDEFGH?
  – tsh
  2 hours ago
  
  

  
  
  
  

 | 
show 1 more comment

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  Interesting... So cutting off adjacent corners will mean they share one corner, and eliminate one edge? This is more complex than it seems at first
  – Jo King
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Since imgur being blocked in Turkey, I can not see the image. Can you please send an alternate image link
  – Windmill Cookies
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @JoKing yes that is correct.
  – infinitezero
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @WindmillCookies I'm sorry, I didn't know that. I've used a different host now.
  – infinitezero
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  For example, may I use 0 for A, 1 for C, 2 for B, 3 for D, 4 for E, 5 for G, 6 for F, 7 for H? Or should I keep the order of ABCDEFGH?
  – tsh
  2 hours ago
  
  

  
  
  
  

2

2

Interesting... So cutting off adjacent corners will mean they share one corner, and eliminate one edge? This is more complex than it seems at first
– Jo King
3 hours ago

Interesting... So cutting off adjacent corners will mean they share one corner, and eliminate one edge? This is more complex than it seems at first
– Jo King
3 hours ago

Since imgur being blocked in Turkey, I can not see the image. Can you please send an alternate image link
– Windmill Cookies
3 hours ago

Since imgur being blocked in Turkey, I can not see the image. Can you please send an alternate image link
– Windmill Cookies
3 hours ago

@JoKing yes that is correct.
– infinitezero
3 hours ago

@JoKing yes that is correct.
– infinitezero
3 hours ago

@WindmillCookies I'm sorry, I didn't know that. I've used a different host now.
– infinitezero
3 hours ago

@WindmillCookies I'm sorry, I didn't know that. I've used a different host now.
– infinitezero
3 hours ago

1

1

For example, may I use 0 for A, 1 for C, 2 for B, 3 for D, 4 for E, 5 for G, 6 for F, 7 for H? Or should I keep the order of ABCDEFGH?
– tsh
2 hours ago

For example, may I use 0 for A, 1 for C, 2 for B, 3 for D, 4 for E, 5 for G, 6 for F, 7 for H? Or should I keep the order of ABCDEFGH?
– tsh
2 hours ago

 | 
show 1 more comment

3 Answers
3

active

oldest

votes

up vote
0
down vote

Perl 6, 59 58 bytes

6+@_,

Try it online!

Uses the numbers 0 to 7 to represent the corners. I probably shpuld have matched them up to the same order as in the question... oops? Outputs a list in the order faces, corners, edges.

share|improve this answer

edited 2 hours ago

answered 3 hours ago

Jo King

18k24199

add a comment | 

up vote
0
down vote

Charcoal, 48 45 bytes

≔Ｅθ↨℅ι²η≔⊘№⭆η⭆ηΣＥι↔⁻§λξν1ηＩＥ⟦⁶⁻⁸η⁻¹²η⟧⁺ι×⊕κＬθ

Try it online! Link is to verbose version of code. Uses digits 0-7 to represent the letters ABDCEFHG in the diagram. Outputs in the order faces, corners, edges. Explanation:

≔Ｅθ↨℅ι²η

Take the ASCII code of each character and convert it to base 2.

≔⊘№⭆η⭆η

Take the cartesian product of the list of base 2 numbers with itself.

ΣＥι↔⁻§λξν1η

XOR the pairs of base 2 numbers together and sum the number of 1 bits. Count how many pairs have a sum of 1 and divide that by 2. This gives the number of coincident corners.

ＩＥ⟦⁶⁻⁸η⁻¹²η⟧⁺ι×⊕κＬθ

Calculate and print the number of faces, corners and edges.

share|improve this answer

edited 2 hours ago

answered 2 hours ago

Neil

77.2k744174

add a comment | 

up vote
0
down vote

JavaScript (Node.js), 84 bytes

a=>[a.map(u=>a.map(v=>j-=!!'ABCDAEFGHEFBCGHD'.match(u+v),n++,j+=2),n=j=6)|2+j,n+j,n]

Try it online!

share|improve this answer

edited 1 hour ago

answered 2 hours ago

tsh

7,95611346

add a comment | 

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3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
0
down vote

Perl 6, 59 58 bytes

6+@_,

Try it online!

Uses the numbers 0 to 7 to represent the corners. I probably shpuld have matched them up to the same order as in the question... oops? Outputs a list in the order faces, corners, edges.

share|improve this answer

edited 2 hours ago

answered 3 hours ago

Jo King

18k24199

add a comment | 

up vote
0
down vote

Perl 6, 59 58 bytes

6+@_,

Try it online!

Uses the numbers 0 to 7 to represent the corners. I probably shpuld have matched them up to the same order as in the question... oops? Outputs a list in the order faces, corners, edges.

share|improve this answer

edited 2 hours ago

answered 3 hours ago

Jo King

18k24199

add a comment | 

up vote
0
down vote

up vote
0
down vote

Perl 6, 59 58 bytes

6+@_,

Try it online!

Uses the numbers 0 to 7 to represent the corners. I probably shpuld have matched them up to the same order as in the question... oops? Outputs a list in the order faces, corners, edges.

share|improve this answer

edited 2 hours ago

answered 3 hours ago

Jo King

18k24199

Perl 6, 59 58 bytes

6+@_,

Try it online!

Uses the numbers 0 to 7 to represent the corners. I probably shpuld have matched them up to the same order as in the question... oops? Outputs a list in the order faces, corners, edges.

share|improve this answer

edited 2 hours ago

answered 3 hours ago

Jo King

18k24199

share|improve this answer

share|improve this answer

edited 2 hours ago

edited 2 hours ago

edited 2 hours ago

answered 3 hours ago

Jo King

18k24199

answered 3 hours ago

Jo King

18k24199

answered 3 hours ago

Jo King

18k24199

18k24199

add a comment | 

add a comment | 

up vote
0
down vote

Charcoal, 48 45 bytes

≔Ｅθ↨℅ι²η≔⊘№⭆η⭆ηΣＥι↔⁻§λξν1ηＩＥ⟦⁶⁻⁸η⁻¹²η⟧⁺ι×⊕κＬθ

Try it online! Link is to verbose version of code. Uses digits 0-7 to represent the letters ABDCEFHG in the diagram. Outputs in the order faces, corners, edges. Explanation:

≔Ｅθ↨℅ι²η

Take the ASCII code of each character and convert it to base 2.

≔⊘№⭆η⭆η

Take the cartesian product of the list of base 2 numbers with itself.

ΣＥι↔⁻§λξν1η

XOR the pairs of base 2 numbers together and sum the number of 1 bits. Count how many pairs have a sum of 1 and divide that by 2. This gives the number of coincident corners.

ＩＥ⟦⁶⁻⁸η⁻¹²η⟧⁺ι×⊕κＬθ

Calculate and print the number of faces, corners and edges.

share|improve this answer

edited 2 hours ago

answered 2 hours ago

Neil

77.2k744174

add a comment | 

up vote
0
down vote

Charcoal, 48 45 bytes

≔Ｅθ↨℅ι²η≔⊘№⭆η⭆ηΣＥι↔⁻§λξν1ηＩＥ⟦⁶⁻⁸η⁻¹²η⟧⁺ι×⊕κＬθ

Try it online! Link is to verbose version of code. Uses digits 0-7 to represent the letters ABDCEFHG in the diagram. Outputs in the order faces, corners, edges. Explanation:

≔Ｅθ↨℅ι²η

Take the ASCII code of each character and convert it to base 2.

≔⊘№⭆η⭆η

Take the cartesian product of the list of base 2 numbers with itself.

ΣＥι↔⁻§λξν1η

XOR the pairs of base 2 numbers together and sum the number of 1 bits. Count how many pairs have a sum of 1 and divide that by 2. This gives the number of coincident corners.

ＩＥ⟦⁶⁻⁸η⁻¹²η⟧⁺ι×⊕κＬθ

Calculate and print the number of faces, corners and edges.

share|improve this answer

edited 2 hours ago

answered 2 hours ago

Neil

77.2k744174

add a comment | 

up vote
0
down vote

up vote
0
down vote

Charcoal, 48 45 bytes

≔Ｅθ↨℅ι²η≔⊘№⭆η⭆ηΣＥι↔⁻§λξν1ηＩＥ⟦⁶⁻⁸η⁻¹²η⟧⁺ι×⊕κＬθ

Try it online! Link is to verbose version of code. Uses digits 0-7 to represent the letters ABDCEFHG in the diagram. Outputs in the order faces, corners, edges. Explanation:

≔Ｅθ↨℅ι²η

Take the ASCII code of each character and convert it to base 2.

≔⊘№⭆η⭆η

Take the cartesian product of the list of base 2 numbers with itself.

ΣＥι↔⁻§λξν1η

XOR the pairs of base 2 numbers together and sum the number of 1 bits. Count how many pairs have a sum of 1 and divide that by 2. This gives the number of coincident corners.

ＩＥ⟦⁶⁻⁸η⁻¹²η⟧⁺ι×⊕κＬθ

Calculate and print the number of faces, corners and edges.

share|improve this answer

edited 2 hours ago

answered 2 hours ago

Neil

77.2k744174

Charcoal, 48 45 bytes

≔Ｅθ↨℅ι²η≔⊘№⭆η⭆ηΣＥι↔⁻§λξν1ηＩＥ⟦⁶⁻⁸η⁻¹²η⟧⁺ι×⊕κＬθ

Try it online! Link is to verbose version of code. Uses digits 0-7 to represent the letters ABDCEFHG in the diagram. Outputs in the order faces, corners, edges. Explanation:

≔Ｅθ↨℅ι²η

Take the ASCII code of each character and convert it to base 2.

≔⊘№⭆η⭆η

Take the cartesian product of the list of base 2 numbers with itself.

ΣＥι↔⁻§λξν1η

XOR the pairs of base 2 numbers together and sum the number of 1 bits. Count how many pairs have a sum of 1 and divide that by 2. This gives the number of coincident corners.

ＩＥ⟦⁶⁻⁸η⁻¹²η⟧⁺ι×⊕κＬθ

Calculate and print the number of faces, corners and edges.

share|improve this answer

edited 2 hours ago

answered 2 hours ago

Neil

77.2k744174

share|improve this answer

share|improve this answer

edited 2 hours ago

edited 2 hours ago

edited 2 hours ago

answered 2 hours ago

Neil

77.2k744174

answered 2 hours ago

Neil

77.2k744174

answered 2 hours ago

Neil

77.2k744174

77.2k744174

add a comment | 

add a comment | 

up vote
0
down vote

JavaScript (Node.js), 84 bytes

a=>[a.map(u=>a.map(v=>j-=!!'ABCDAEFGHEFBCGHD'.match(u+v),n++,j+=2),n=j=6)|2+j,n+j,n]

Try it online!

share|improve this answer

edited 1 hour ago

answered 2 hours ago

tsh

7,95611346

add a comment | 

up vote
0
down vote

JavaScript (Node.js), 84 bytes

a=>[a.map(u=>a.map(v=>j-=!!'ABCDAEFGHEFBCGHD'.match(u+v),n++,j+=2),n=j=6)|2+j,n+j,n]

Try it online!

share|improve this answer

edited 1 hour ago

answered 2 hours ago

tsh

7,95611346

add a comment | 

up vote
0
down vote

up vote
0
down vote

JavaScript (Node.js), 84 bytes

a=>[a.map(u=>a.map(v=>j-=!!'ABCDAEFGHEFBCGHD'.match(u+v),n++,j+=2),n=j=6)|2+j,n+j,n]

Try it online!

share|improve this answer

edited 1 hour ago

answered 2 hours ago

tsh

7,95611346

JavaScript (Node.js), 84 bytes

a=>[a.map(u=>a.map(v=>j-=!!'ABCDAEFGHEFBCGHD'.match(u+v),n++,j+=2),n=j=6)|2+j,n+j,n]

Try it online!

share|improve this answer

edited 1 hour ago

answered 2 hours ago

tsh

7,95611346

share|improve this answer

share|improve this answer

edited 1 hour ago

edited 1 hour ago

edited 1 hour ago

answered 2 hours ago

tsh

7,95611346

answered 2 hours ago

tsh

7,95611346

answered 2 hours ago

tsh

7,95611346

7,95611346

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