Credibility theory: Difference between revisions
Jump to navigation
Jump to search
en>Melcombe →References: add cat |
en>Yobot m WP:CHECKWIKI error fixes using AWB (9475) |
||
| Line 1: | Line 1: | ||
{{Uniform polyhedra db|Uniform polyhedron stat table|tDD}} | |||
In [[geometry]], the '''truncated dodecadodecahedron''' is a [[nonconvex uniform polyhedron]], indexed as U<sub>59</sub>. It is given a [[Schläfli symbol]] t<sub>0,1,2</sub>{5/3,5}. It has 120 vertices and 54 faces: 30 squares, 12 [[decagon]]s, and 12 [[Decagram (geometry)|decagrams]]. The central region of the polyhedron is connected to the exterior via 20 small triangular holes. | |||
The name ''truncated dodecadodecahedron'' is somewhat misleading: truncation of the [[dodecadodecahedron]] would produce rectangular faces rather than squares, and the pentagram faces of the dodecahedron would turn into truncated pentagrams rather than decagrams. However, it is the quasitruncation of the dodecadodecahedron, as defined by {{harvtxt|Coxeter|Longuet-Higgins|Miller|1954}}.<ref>{{citation | |||
| last1 = Coxeter | first1 = H. S. M. | author1-link = Harold Scott MacDonald Coxeter | |||
| last2 = Longuet-Higgins | first2 = M. S. | author2-link = Michael S. Longuet-Higgins | |||
| last3 = Miller | first3 = J. C. P. | author3-link = J. C. P. Miller | |||
| journal = Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences | |||
| jstor = 91532 | |||
| mr = 0062446 | |||
| pages = 401–450 | |||
| title = Uniform polyhedra | |||
| volume = 246 | |||
| year = 1954 | doi=10.1098/rsta.1954.0003}}. See especially the description as a quasitruncation on p. 411 and the photograph of a model of its skeleton in Fig. 114, Plate IV.</ref> For this reason, it is also known as the '''quasitruncated dodecadodecahedron'''.<ref>Wenninger writes "quasitruncated dodecahedron", but this appear to be a mistake. {{citation|contribution=98 Quasitruncated dodecahedron|pages=152–153|first=Magnus J.|last=Wenninger|authorlink=Magnus Wenninger|title=Polyhedron Models|publisher=Cambridge University Press|year=1971}}.</ref> Coxeter et al. credit its discovery to a paper published in 1881 by Austrian mathematician Johann Pitsch.<ref>{{citation | |||
| last = Pitsch | first = Johann | |||
| journal = Zeitschrift für das Realschulwesen | |||
| pages = 9–24, 72–89, 216 | |||
| title = Über halbreguläre Sternpolyeder | |||
| volume = 6 | |||
| year = 1881}}. According to {{harvtxt|Coxeter|Longuet-Higgins|Miller|1954}}, the truncated dodecadodecahedron appears as no. XII on p.86.</ref> | |||
== Cartesian coordinates == | |||
[[Cartesian coordinates]] for the vertices of a truncated dodecadodecahedron are all the triples of numbers obtained by circular shifts and sign changes from the following points (where <math>\varphi = \frac{1 + \sqrt{5}}{2}</math> is the [[golden ratio]]): | |||
:<math>(1,1,3);\quad | |||
(\frac{1}{\varphi}, \frac{1}{\varphi^2}, 2\varphi);\quad | |||
(\varphi, \frac{2}{\varphi}, \varphi^2);\quad | |||
(\varphi^2, \frac{1}{\varphi^2}, 2);\quad | |||
(2\varphi-1,1,2\varphi-1).</math> | |||
Each of these five points has eight possible sign patterns and three possible circular shifts, giving a total of 120 different points. | |||
==As a Cayley graph== | |||
The truncated dodecadodecahedron forms a [[Cayley graph]] for the [[symmetric group]] on five elements, as generated by two group members: one that swaps the first two elements of a five-tuple, and one that performs a [[circular shift]] operation on the last four elements. That is, the 120 vertices of the polyhedron may be placed in one-to-one correspondence with the 5! [[permutations]] on five elements, in such a way that the three neighbors of each vertex are the three permutations formed from it by swapping the first two elements or circularly shifting (in either direction) the last four elements.<ref>{{citation | |||
| last = Eppstein | first = David | authorlink = David Eppstein | |||
| editor1-last = Tollis | editor1-first = Ioannis G. | |||
| editor2-last = Patrignani | editor2-first = Marizio | |||
| arxiv = 0709.4087 | |||
| contribution = The topology of bendless three-dimensional orthogonal graph drawing | |||
| doi = 10.1007/978-3-642-00219-9_9 | |||
| location = Heraklion, Crete | |||
| pages = 78–89 | |||
| publisher = Springer-Verlag | |||
| series = Lecture Notes in Computer Science | |||
| title = Proc. 16th Int. Symp. Graph Drawing | |||
| volume = 5417 | |||
| year = 2008}}.</ref> | |||
== See also == | |||
* [[List of uniform polyhedra]] | |||
==References== | |||
{{reflist}} | |||
== External links == | |||
* {{mathworld | urlname = TruncatedDodecadodecahedron| title = Truncated dodecadodecahedron}} | |||
[[Category:Uniform polyhedra]] | |||
Revision as of 22:13, 10 September 2013
Template:Uniform polyhedra db In geometry, the truncated dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U59. It is given a Schläfli symbol t0,1,2{5/3,5}. It has 120 vertices and 54 faces: 30 squares, 12 decagons, and 12 decagrams. The central region of the polyhedron is connected to the exterior via 20 small triangular holes.
The name truncated dodecadodecahedron is somewhat misleading: truncation of the dodecadodecahedron would produce rectangular faces rather than squares, and the pentagram faces of the dodecahedron would turn into truncated pentagrams rather than decagrams. However, it is the quasitruncation of the dodecadodecahedron, as defined by Template:Harvtxt.[1] For this reason, it is also known as the quasitruncated dodecadodecahedron.[2] Coxeter et al. credit its discovery to a paper published in 1881 by Austrian mathematician Johann Pitsch.[3]
Cartesian coordinates
Cartesian coordinates for the vertices of a truncated dodecadodecahedron are all the triples of numbers obtained by circular shifts and sign changes from the following points (where is the golden ratio):
Each of these five points has eight possible sign patterns and three possible circular shifts, giving a total of 120 different points.
As a Cayley graph
The truncated dodecadodecahedron forms a Cayley graph for the symmetric group on five elements, as generated by two group members: one that swaps the first two elements of a five-tuple, and one that performs a circular shift operation on the last four elements. That is, the 120 vertices of the polyhedron may be placed in one-to-one correspondence with the 5! permutations on five elements, in such a way that the three neighbors of each vertex are the three permutations formed from it by swapping the first two elements or circularly shifting (in either direction) the last four elements.[4]
See also
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
External links
- 22 year-old Systems Analyst Rave from Merrickville-Wolford, has lots of hobbies and interests including quick cars, property developers in singapore and baking. Always loves visiting spots like Historic Monuments Zone of Querétaro.
Here is my web site - cottagehillchurch.com
- ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. See especially the description as a quasitruncation on p. 411 and the photograph of a model of its skeleton in Fig. 114, Plate IV. - ↑ Wenninger writes "quasitruncated dodecahedron", but this appear to be a mistake. Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. - ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. According to Template:Harvtxt, the truncated dodecadodecahedron appears as no. XII on p.86. - ↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.
Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.
In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.
Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region
Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.
15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.
To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.