918:(5) A logical explanation (hinted at in the above link) is that the square faces came as the result of distortion into a "rhombic" shape (i.e., their square shape, which are quadrilaterals with equal-length sides) after the solid was generated by a geometric operation, such as expansion. For example, the rhombi-truncated cuboctahedron is generated by truncation of the cuboctahedron, but this leaves rectangles instead of square faces. The "rhombi-" prefix clarifies that the truncated shape must be deformed into the Archimedean solid that has square faces instead of rectangles. You can easily find an explanation like this for all solids that have "rhomb" in their names or alternate names.
921:(6) It just seems odd that the coincidence of planes for some faces should justify a name, when there's often no other direct connection to the named-after solid, especially when there are usually many other solids with closer geometrical connections that did not affect the naming of the new solid. For example, there are many solids that have faces that lie in the same plane as dodecahedra (or tetrahedra, or cubes), yet they don't have some form or portion of the word "dodecahedron" (or "tetrahedron," or "cube") in their name. If anyone can confirm the information as written, please do so. Otherwise, I may change the text and cite the link I have provided above.
84:
74:
53:
176:
158:
22:
906:. This page says, "What does rhombi mean in the name of a polyhedron? Answer: The true answer to this is a bit complex. Students should make a connection between the red (medium shaded) squares that arise in the polyhedra with rhombi in the naming. You could make the connection that the etymology of rhombi meant a square."
897:
On several
Knowledge pages, regarding the naming of solids, it is claimed—in all instances, without citation—that the prefix "rhombi-" comes from the fact that some or all of the faces of the solid in question lie in the same plane as the faces of another solid (e.g., the rhombic dodecahedron) that
802:
909:(2) The most obvious meaning of "rhomb-" is related to squares or rhombuses (rhombi). All the polyhedra with "rhomb-" prefixes have square faces. (And there's something special about them, which I'll explain later.)
912:(3) An alternate name for the cuboctahedron is "rhombitetratetrahedron," but the cuboctahedron does not have any set of faces that happen to lie in the same plane as another solid with "rhombic" in its name.
673:
605:
247:
Somebody should make a soccer ball shaped like this ^_^ Of course, it would be much more expensive...but would look so much cooler! I wonder if the aerodynamics would be significantly different...?
527:
457:
898:
happens to have the name "rhombic" in it. I think this can be shown to be specious (even though I've found this claim on one non-Knowledge page, but also unsourced there) for several reasons:
140:
387:
915:(4) I'm guessing (but can't source this) that many of the "rhombi-" names were in use BEFORE the names of the solids that supposedly gave rise to their "rhomb-" prefixes.
960:
224:
876:
950:
230:
130:
945:
718:
955:
106:
200:
858:
812:
97:
58:
883:
183:
163:
611:
533:
463:
393:
33:
877:
https://www.slideshare.net/hcr1991/mathematical-analysis-of-great-rhombicosidodecahedron-the-largest-archimedean-solid/
879:
809:
Please check the calculation, it is quite simple, and if I am right, correct the formula (and remove this talk).
330:
21:
816:
324:
If we multiply everything by φ, the edge length becomes 2 and the coordinates are the even permutations of
39:
83:
265:
I'll change them when I happen to visit the pages ... or maybe, who knows, I'll get ambitious. ;) —
199:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
105:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
89:
827:
73:
52:
255:
I don't care, didn't add the original term, but it is used ALL over, if you want to change it.
866:
698:
683:
305:
283:
713:
The solid has 30 square, 20 hexagonal and 12 decagonal faces in total, so its area should be
175:
157:
926:
838:
930:
887:
870:
820:
702:
687:
309:
287:
269:
259:
939:
903:
862:
694:
679:
301:
279:
266:
256:
797:{\displaystyle A_{O}=30a^{2}\left(1+{\sqrt {3}}+{\sqrt {5+2{\sqrt {5}}}}\right)}
102:
922:
79:
196:
192:
829:, and comes out to 175.031044596 by my calculator, while a reference book
831:
The
Geometrical Foundation of Natural Structure: A Source Book of Design
188:
15:
861:, although it would be better to have SOURCE to reference!
833:, shows a decimal 174.2880, close!?. How hard could it be!?
668:{\displaystyle (\pm \phi ^{2},\pm 3\phi ,\pm 2\phi ^{2})}
600:{\displaystyle (\pm (\phi +2),\pm 2\phi ,\pm (3\phi +1))}
721:
614:
536:
466:
396:
333:
522:{\displaystyle (\pm 1,\pm \phi ^{3},\pm (2\phi +3))}
452:{\displaystyle (\pm 2,\pm \phi ^{2},\pm (3\phi +2))}
187:, a collaborative effort to improve the coverage of
101:, a collaborative effort to improve the coverage of
904:http://www.geom.uiuc.edu/~teach95/kt95/KTL12t.html
796:
667:
599:
521:
451:
381:
229:This article has not yet received a rating on the
826:The formula used now is referenced on Mathworld
8:
382:{\displaystyle (\pm 1,\pm 1,\pm (4\phi +1))}
19:
850:12 {10} - 10/(4*tan(pi/10))*12 = 92.330506
806:It is equal to 174.2920303 in estimation.
152:
47:
780:
769:
759:
742:
726:
720:
656:
625:
613:
535:
486:
465:
416:
395:
332:
847:20 {6} - 6/(4*tan(pi/6))*20 = 51.961524
844:30 {4} - 4/(4*tan(pi/4))*30 = 1*30 = 30
154:
49:
278:I wonder what we both meant by that. —
961:Unknown-importance Polyhedra articles
7:
181:This article is within the scope of
95:This article is within the scope of
893:The meaning and origin of "rhombi-"
38:It is of interest to the following
14:
951:Low-priority mathematics articles
841:, edge length 1 = n/(4*tan(pi/n))
115:Knowledge:WikiProject Mathematics
946:Start-Class mathematics articles
174:
156:
118:Template:WikiProject Mathematics
82:
72:
51:
20:
209:Knowledge:WikiProject Polyhedra
135:This article has been rated as
956:Start-Class Polyhedra articles
875:I don't think so, look here :
662:
615:
594:
591:
576:
555:
543:
537:
516:
513:
498:
467:
446:
443:
428:
397:
376:
373:
358:
334:
212:Template:WikiProject Polyhedra
1:
931:01:28, 24 February 2017 (UTC)
203:and see a list of open tasks.
109:and see a list of open tasks.
270:18:24, 7 February 2006 (UTC)
260:06:20, 7 February 2006 (UTC)
871:02:21, 1 January 2015 (UTC)
821:00:21, 1 January 2015 (UTC)
977:
703:17:41, 20 April 2018 (UTC)
688:04:58, 20 April 2018 (UTC)
310:17:41, 20 April 2018 (UTC)
288:04:58, 20 April 2018 (UTC)
231:project's importance scale
857:So I'm in agreement with
709:Error in the area formula
228:
169:
134:
67:
46:
888:13:18, 3 July 2017 (UTC)
141:project's priority scale
320:to put that another way
98:WikiProject Mathematics
798:
669:
601:
523:
453:
383:
28:This article is rated
839:Area of regular n-gon
799:
670:
602:
524:
454:
384:
251:Cartesian coordinates
184:WikiProject Polyhedra
719:
612:
534:
464:
394:
331:
121:mathematics articles
794:
693:I'd go with that!
665:
597:
519:
449:
379:
215:Polyhedra articles
90:Mathematics portal
34:content assessment
787:
785:
764:
245:
244:
241:
240:
237:
236:
151:
150:
147:
146:
968:
880:InternetowyGołąb
803:
801:
800:
795:
793:
789:
788:
786:
781:
770:
765:
760:
747:
746:
731:
730:
674:
672:
671:
666:
661:
660:
630:
629:
606:
604:
603:
598:
528:
526:
525:
520:
491:
490:
458:
456:
455:
450:
421:
420:
388:
386:
385:
380:
217:
216:
213:
210:
207:
178:
171:
170:
160:
153:
123:
122:
119:
116:
113:
92:
87:
86:
76:
69:
68:
63:
55:
48:
31:
25:
24:
16:
976:
975:
971:
970:
969:
967:
966:
965:
936:
935:
895:
853:Total 174.29203
752:
748:
738:
722:
717:
716:
711:
652:
621:
610:
609:
532:
531:
482:
462:
461:
412:
392:
391:
329:
328:
322:
253:
214:
211:
208:
205:
204:
120:
117:
114:
111:
110:
88:
81:
61:
32:on Knowledge's
29:
12:
11:
5:
974:
972:
964:
963:
958:
953:
948:
938:
937:
934:
933:
919:
916:
913:
910:
907:
894:
891:
855:
854:
851:
848:
845:
842:
835:
834:
792:
784:
779:
776:
773:
768:
763:
758:
755:
751:
745:
741:
737:
734:
729:
725:
710:
707:
706:
705:
676:
675:
664:
659:
655:
651:
648:
645:
642:
639:
636:
633:
628:
624:
620:
617:
607:
596:
593:
590:
587:
584:
581:
578:
575:
572:
569:
566:
563:
560:
557:
554:
551:
548:
545:
542:
539:
529:
518:
515:
512:
509:
506:
503:
500:
497:
494:
489:
485:
481:
478:
475:
472:
469:
459:
448:
445:
442:
439:
436:
433:
430:
427:
424:
419:
415:
411:
408:
405:
402:
399:
389:
378:
375:
372:
369:
366:
363:
360:
357:
354:
351:
348:
345:
342:
339:
336:
321:
318:
317:
316:
315:
314:
313:
312:
293:
292:
291:
290:
273:
272:
252:
249:
243:
242:
239:
238:
235:
234:
227:
221:
220:
218:
201:the discussion
179:
167:
166:
161:
149:
148:
145:
144:
133:
127:
126:
124:
107:the discussion
94:
93:
77:
65:
64:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
973:
962:
959:
957:
954:
952:
949:
947:
944:
943:
941:
932:
928:
924:
920:
917:
914:
911:
908:
905:
901:
900:
899:
892:
890:
889:
885:
881:
878:
873:
872:
868:
864:
860:
859:31.11.242.188
852:
849:
846:
843:
840:
837:
836:
832:
828:
825:
824:
823:
822:
818:
814:
813:31.11.242.188
810:
807:
804:
790:
782:
777:
774:
771:
766:
761:
756:
753:
749:
743:
739:
735:
732:
727:
723:
714:
708:
704:
700:
696:
692:
691:
690:
689:
685:
681:
657:
653:
649:
646:
643:
640:
637:
634:
631:
626:
622:
618:
608:
588:
585:
582:
579:
573:
570:
567:
564:
561:
558:
552:
549:
546:
540:
530:
510:
507:
504:
501:
495:
492:
487:
483:
479:
476:
473:
470:
460:
440:
437:
434:
431:
425:
422:
417:
413:
409:
406:
403:
400:
390:
370:
367:
364:
361:
355:
352:
349:
346:
343:
340:
337:
327:
326:
325:
319:
311:
307:
303:
299:
298:
297:
296:
295:
294:
289:
285:
281:
277:
276:
275:
274:
271:
268:
264:
263:
262:
261:
258:
250:
248:
232:
226:
223:
222:
219:
202:
198:
194:
190:
186:
185:
180:
177:
173:
172:
168:
165:
162:
159:
155:
142:
138:
132:
129:
128:
125:
108:
104:
100:
99:
91:
85:
80:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
896:
874:
856:
830:
811:
808:
805:
715:
712:
677:
323:
254:
246:
195:, and other
182:
137:Low-priority
136:
96:
62:Low‑priority
40:WikiProjects
112:Mathematics
103:mathematics
59:Mathematics
30:Start-class
940:Categories
206:Polyhedra
197:polytopes
193:polyhedra
164:Polyhedra
902:(1) See
863:Tom Ruen
695:Tom Ruen
302:Tom Ruen
300:Indeed!
257:Tom Ruen
189:polygons
680:Tamfang
280:Tamfang
267:Tamfang
139:on the
36:scale.
927:talk
923:Holy
884:talk
867:talk
817:talk
699:talk
684:talk
306:talk
284:talk
225:???
131:Low
942::
929:)
886:)
869:)
819:)
736:30
701:)
686:)
654:ϕ
647:±
641:ϕ
635:±
623:ϕ
619:±
583:ϕ
574:±
568:ϕ
562:±
547:ϕ
541:±
505:ϕ
496:±
484:ϕ
480:±
471:±
435:ϕ
426:±
414:ϕ
410:±
401:±
365:ϕ
356:±
347:±
338:±
308:)
286:)
191:,
925:(
882:(
865:(
815:(
791:)
783:5
778:2
775:+
772:5
767:+
762:3
757:+
754:1
750:(
744:2
740:a
733:=
728:O
724:A
697:(
682:(
678:—
663:)
658:2
650:2
644:,
638:3
632:,
627:2
616:(
595:)
592:)
589:1
586:+
580:3
577:(
571:,
565:2
559:,
556:)
553:2
550:+
544:(
538:(
517:)
514:)
511:3
508:+
502:2
499:(
493:,
488:3
477:,
474:1
468:(
447:)
444:)
441:2
438:+
432:3
429:(
423:,
418:2
407:,
404:2
398:(
377:)
374:)
371:1
368:+
362:4
359:(
353:,
350:1
344:,
341:1
335:(
304:(
282:(
233:.
143:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
