Elongated pentagonal orthocupolarotunda

Elongated pentagonal orthocupolarotunda

Type	Johnson $J 39 - J 40 - J 41$
Faces	3x5 triangles 3x5 squares 2+5 pentagons
Edges	70
Vertices	35
Vertex configuration	$10(3.4 3) 10(3.4 2 .5) 5(3.4.5.4) 2.5(3.5.3.5)$
Symmetry group	$C 5v$
Dual polyhedron	-
Properties	convex
Net

In geometry, the elongated pentagonal orthocupolarotunda is one of the Johnson solids ( $J 40$ ). As the name suggests, it can be constructed by elongating a pentagonal orthocupolarotunda ( $J 32$ ) by inserting a decagonal prism between its halves. Rotating either the cupola or the rotunda through 36 degrees before inserting the prism yields an elongated pentagonal gyrocupolarotunda ( $J 41$ ).

A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.^[1]

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:^[2]

V={\frac {5}{12}}\left(11+5{\sqrt {5}}+6{\sqrt {5+2{\sqrt {5}}}}\right)a^{3}\approx 16.936...a^{3}

A={\frac {1}{4}}\left(60+{\sqrt {10\left(190+49{\sqrt {5}}+21{\sqrt {75+30{\sqrt {5}}}}\right)}}\right)a^{2}\approx 33.5385...a^{2}

References

^ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.
^ Stephen Wolfram, "Elongated pentagonal orthocupolarotunda" from Wolfram Alpha. Retrieved July 25, 2010.

External links

Weisstein, Eric W., "Elongated pentagonal orthocupolarotunda" ("Johnson solid") at MathWorld.

v t e Johnson solids
Pyramids, cupolae and rotundae	square pyramid pentagonal pyramid triangular cupola square cupola pentagonal cupola pentagonal rotunda
Modified pyramids	elongated triangular pyramid elongated square pyramid elongated pentagonal pyramid gyroelongated square pyramid gyroelongated pentagonal pyramid triangular bipyramid pentagonal bipyramid elongated triangular bipyramid elongated square bipyramid elongated pentagonal bipyramid gyroelongated square bipyramid
Modified cupolae and rotundae	elongated triangular cupola elongated square cupola elongated pentagonal cupola elongated pentagonal rotunda gyroelongated triangular cupola gyroelongated square cupola gyroelongated pentagonal cupola gyroelongated pentagonal rotunda gyrobifastigium triangular orthobicupola square orthobicupola square gyrobicupola pentagonal orthobicupola pentagonal gyrobicupola pentagonal orthocupolarotunda pentagonal gyrocupolarotunda pentagonal orthobirotunda elongated triangular orthobicupola elongated triangular gyrobicupola elongated square gyrobicupola elongated pentagonal orthobicupola elongated pentagonal gyrobicupola elongated pentagonal orthocupolarotunda elongated pentagonal gyrocupolarotunda elongated pentagonal orthobirotunda elongated pentagonal gyrobirotunda gyroelongated triangular bicupola gyroelongated square bicupola gyroelongated pentagonal bicupola gyroelongated pentagonal cupolarotunda gyroelongated pentagonal birotunda
Augmented prisms	augmented triangular prism biaugmented triangular prism triaugmented triangular prism augmented pentagonal prism biaugmented pentagonal prism augmented hexagonal prism parabiaugmented hexagonal prism metabiaugmented hexagonal prism triaugmented hexagonal prism
Modified Platonic solids	augmented dodecahedron parabiaugmented dodecahedron metabiaugmented dodecahedron triaugmented dodecahedron metabidiminished icosahedron tridiminished icosahedron augmented tridiminished icosahedron
Modified Archimedean solids	augmented truncated tetrahedron augmented truncated cube biaugmented truncated cube augmented truncated dodecahedron parabiaugmented truncated dodecahedron metabiaugmented truncated dodecahedron triaugmented truncated dodecahedron gyrate rhombicosidodecahedron parabigyrate rhombicosidodecahedron metabigyrate rhombicosidodecahedron trigyrate rhombicosidodecahedron diminished rhombicosidodecahedron paragyrate diminished rhombicosidodecahedron metagyrate diminished rhombicosidodecahedron bigyrate diminished rhombicosidodecahedron parabidiminished rhombicosidodecahedron metabidiminished rhombicosidodecahedron gyrate bidiminished rhombicosidodecahedron tridiminished rhombicosidodecahedron
Other elementary solids	snub disphenoid snub square antiprism sphenocorona augmented sphenocorona sphenomegacorona hebesphenomegacorona disphenocingulum bilunabirotunda triangular hebesphenorotunda
(See also List of Johnson solids, a sortable table)

This polyhedron-related article is a stub. You can help Wikipedia by expanding it.

Read other articles:

Katherine Maher

Katherine MaherKatherine Maher, 2016 Direktur Eksekutif Yayasan Wikimedia ke-4Masa jabatan23 Juni 2016 – 15 April 2021Ad interim: 14 Maret – 23 Juni 2016 PendahuluLila TretikovPenggantiPetahana Informasi pribadiLahir18 April 1983 (umur 40) Wilton, ConnecticutKebangsaanAmerika SerikatAlma materUniversitas New YorkPekerjaanEksekutif non-profit Maher introducing herself recorded June 2016 Sunting kotak info • L • B Katherine Roberts Maher (/mɑːr/;[1] lah...

Dirgantara Air Service Penerbangan 5940

Dirgantara Air Service Penerbangan 5940Sebuah CASA C-212 Aviocar, jenis yang sama dengan pesawat yang mengalami kecelakaanRingkasan kecelakaanTanggal7 Desember 1996 (1996-12-07)RingkasanKegagalan mesin saat lepas landasLokasiDekat Bandar Udara Internasional Syamsudin Noor , Banjarmasin, Kalimantan Selatan, IndonesiaPenumpang15 (termasuk 1 anak)Awak2Cedera3 (termasuk 2 di tanah)Tewas18 (termasuk 2 di tanah)Selamat1 (awalnya 2)Jenis pesawatCASA C-212 AviocarOperatorDirgantara Air Serv...

App Store (iOS)

App StoreTipetoko aplikasi dan organisasi Versi pertama10 Juli 2008; 15 tahun lalu (2008-07-10)GenreDistribusi digital, pemutakhiran perangkat lunakLisensiPerangkat lunak gratis proprieterKarakteristik teknisSistem operasiiOS, iTunes 8 atau yang terbaruPlatformiPod Touch Informasi pengembangPengembangAppleInformasi tambahanSitus webwww.apple.com/iphone/from-the-app-store/ Sunting di Wikidata • L • B • Bantuan penggunaan templat ini Ikon lama App Store App Store adala...

1974 World Men's Handball Championship

1974 World Men's Handball ChampionshipTournament detailsHost country East GermanyDates28 February-10 March 1974Teams16Final positionsChampions RomaniaRunner-up East GermanyThird place YugoslaviaTournament statisticsMatches played42Goals scored1,556 (37.05 per match)← PreviousNext → The 1974 World Men's Handball Championship was the eighth team handball World Championship. It was held in East Germany between 28 February-10 March 197...

Tourbe

Pour les articles homonymes, voir Tourbe (homonymie). Si ce bandeau n'est plus pertinent, retirez-le. Cliquez ici pour en savoir plus. Cet article ne cite pas suffisamment ses sources (septembre 2009). Si vous disposez d'ouvrages ou d'articles de référence ou si vous connaissez des sites web de qualité traitant du thème abordé ici, merci de compléter l'article en donnant les références utiles à sa vérifiabilité et en les liant à la section « Notes et références ». E...

Ram Kapoor

Ram KapoorKapoor pada pembukaan acaranya Bade Achhe Lagte HainLahirRaam Anil Kapoor1 September 1973 (umur 50)[1]New Delhi, IndiaKebangsaanIndianPekerjaanaktorTahun aktif1997–sekarangDikenal atasManshaa,Kasamh Se, Bade Achhe Lagte Hain , Dil Ki Baatein Dil Hi Jaane dan HumshakalsSuami/istriGautami Kapoor (m. 2003)AnakAks Kapoor (anak laki-laki)Sia Kapoor (anak perempuan)Orang tuaRita Kapoor (Ibu)Anil Kapoor (Ayah) Ram Kapoor ([raːm kəpuːr]...

Jodie Comer

Jodie Comer (2023) Jodie Marie Comer (Liverpool, 11 marzo 1993) è un'attrice britannica. È nota per il ruolo di Villanelle nella serie televisiva Killing Eve (2018-22), per la quale si aggiudica il BAFTA Television Award e il Premio Emmy nella sezione miglior attrice in una serie drammatica, venendo inoltre nominata due volte al Golden Globe, due al Critics Choice Television Award e una allo Screen Actors Guild Award. Nel 2022 ha vinto il Critics Choice Super Award perThe Last Duel di Ridle...

2015 Philadelphia mayoral election

2015 mayoral election in Philadelphia, Pennsylvania 2015 Philadelphia mayoral election ← 2011 November 3, 2015 2019 → Turnout21.84%[1] Nominee Jim Kenney Melissa Murray Bailey Party Democratic Republican Popular vote 203,730 31,563 Percentage 85.1% 13.2% Results by wardKenney: 60–70% 70–80% 80–90% >90% Mayor before election ...

Goya Award for Best Director

Spanish national film award Goya Award for Best DirectorAwarded forBest Director of the YearCountrySpainPresented byAcademia de las Artes y las Ciencias Cinematográficas de EspañaCurrently held byJ. A. Bayona for Society of the Snow (2023)Websitehttp://www.premiosgoya.com/ The Goya Award for Best Director (Spanish: Premio Goya a la mejor dirección) is one of the Goya Awards, Spain's principal national film awards. The category has been presented ever since the first edition of the Goya Awa...

الاتحاد الصحراوي لكرة القدم

هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (يونيو 2018) الاتحاد الصحراوي لكرة القدم الرياضة كرة القدم أسس عام 1989 المقر العيون تعديل مصدري - تعديل الاتحاد الصحراوي لكرة القدم (بالإسبانية: Federación Saharaui de...

Rex Perpetuus Norvegiae

Ilustrasi Saga Olav den helliges (1899) Rex Perpetuus Norvegiae (bahasa Latin), yaitu Raja Abadi Norwegia) merupakan istilah untuk Raja Olaf II dari Norwegia yang juga dikenal sebagai St. Olaf (Olav den hellige) .[1][2] Latar belakang Dalam sumber tertulis, istilah Perpetuus rex Norvegiæ muncul dari paruh kedua abad ke-12 di Historia Norvegiæ.[3] Hukum Suksesi 1163 (Tronfølgeloven av 1163) menyatakan bahwa semua raja setelah Raja Magnus I, putra Olaf II, harus dilih...

Філософія

Частина серії проФілософіяLeft to right: Plato, Kant, Nietzsche, Buddha, Confucius, AverroesПлатонКантНіцшеБуддаКонфуційАверроес Філософи Епістемологи Естетики Етики Логіки Метафізики Соціально-політичні філософи Традиції Аналітична Арістотелівська Африканська Близькосхідна іранська Буддій�...

Alison Waley

Alison WaleyBorn(1901-04-29)29 April 1901Nelson, New ZealandDied10 May 2001(2001-05-10) (aged 100)Highgate, London, United KingdomNationalityNew ZealandOccupation(s)Poet, journalist, artist, writerNotable workA Half of Two Lives: A Personal Memoir Alison Grant Robinson Waley (29 April 1901 – 10 May 2001) was a New Zealand poet, journalist, artist and writer,[1] best known for her memoir A Half of Two Lives: A Personal Memoir,[2] a book about her lifelong affair with wr...

1964 United States House of Representatives elections

House elections for the 89th U.S. Congress 1964 United States House of Representatives elections ← 1962 November 3, 1964 1966 → All 435 seats in the United States House of Representatives218 seats needed for a majority Majority party Minority party Leader John McCormack Charles Halleck Party Democratic Republican Leader since January 10, 1962 January 3, 1959 Leader's seat Massachusetts 9th Indiana 2nd Last election 259 seats 176 sea...

The 4th Act

Documentary film about the community of Ballymun in north Dublin This article is an orphan, as no other articles link to it. Please introduce links to this page from related articles; try the Find link tool for suggestions. (December 2023) 4th ActDirected byTurlough KellyProduced byAndrew KeoghCinematographyJohn BreslinEdited byTurlough Kelly & Andrew KeoghMusic byChristopher GI BuckleyProductioncompanyBread & CircusDistributed byWildcardRelease date 2017 (2017) Running time75 mi...

Daftar Wakil Bupati Pidie Jaya

Wakil Bupati Pidie JayaPetahanaSaid Mulyadi, S.E., M.Si.sejak 4 Februari 2019Masa jabatan5 tahunDibentuk2 Februari 2009Pejabat pertamaH. M. Yusuf IbrahimSitus webwww.pidiejayakab.go.id Berikut ini adalah daftar Wakil Bupati Pidie Jaya dari masa ke masa. No Wakil Bupati Mulai Jabatan Akhir Jabatan Prd. Ket. Bupati 1 H. M.Yusuf Ibrahim 2 Februari 2009 2 Februari 2014 1 Drs. H. M.Gade Salam 2 H.Said MulyadiS.E., M.Si. 3 Februari 2014 15 Februari 2018 2 [Ket. 1] H.Aiyub Abbas ...

Unmasked (Kiss album)

1980 studio album by Kiss UnmaskedCover art by Victor StabinStudio album by KissReleasedMay 20, 1980 (1980-05-20)RecordedJanuary–March 1980StudioThe Record Plant, New York CityGenreHard rockpop rockpower popLength39:46LabelCasablancaProducerVini PonciaKiss chronology Dynasty(1979) Unmasked(1980) Music from The Elder(1981) Singles from Unmasked ShandiReleased: June 1, 1980 Talk to MeReleased: August 24, 1980 TomorrowReleased: November 1, 1980 Unmasked is the eighth studio ...

يندلي ميلر غاريسون

يندلي ميلر غاريسون معلومات شخصية الميلاد 28 نوفمبر 1864 كامدن الوفاة 19 أكتوبر 1932 (67 سنة) سي برايت مواطنة الولايات المتحدة الحياة العملية المدرسة الأم جامعة هارفاردكلية الحقوق في جامعة بنسيلفانيا [لغات أخرى]‏أكاديمية فيلبس إيكستر [لغات أخر�...

A proposito di Davis

A proposito di DavisOscar Isaac in una scena del filmTitolo originaleInside Llewyn Davis Lingua originaleinglese Paese di produzioneStati Uniti d'America, Francia Anno2013 Durata105 min Rapporto1,85:1 Generedrammatico, commedia RegiaJoel ed Ethan Coen SceneggiaturaJoel ed Ethan Coen ProduttoreJoel ed Ethan Coen, Scott Rudin Produttore esecutivoOlivier Courson, Robert Graf, Ron Halpern Casa di produzioneStudioCanal, Anton Capital Entertainment, Mike Zoss Productions, Scott Rudin Produc...

Rideau Centre

Shopping mall in Ottawa, Ontario, Canada This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Rideau Centre – news · newspapers · books · scholar · JSTOR (December 2012) (Learn how and when to remove this message) CF Rideau CentreRideau Centre entrance, 2019Coordinates45°25′27″N 75°41′27″W / &#x...